77.17 Breyting á topppunkti

7.17.5 Jöfnur grafhliðrana

7.17.5 • Jöfnur grafhliðrana

Lokaverkefni

Hér er graf sem táknar fallið:

f(x) = x²

A graph of the parent quadratic function is given in blue on the coordinate plane. The x-axis extends from negative 6 to 6 with a scale of 2. The y-axis extends from negative 30 to 30 with a scale of 10.

Notaðu grafteikniverkfæri eða aðra tækni. Teiknaðu í sama hnitakerfi graf sem táknar fallið:

f(x) = (x − 6)² + 10

Berðu saman svarið þitt:

A graph of the parent quadratic function is given in blue on the coordinate plane. The graph of a second parabola is given and labeled with a vertex at the point (6, 10).

Grafið hefur sömu lögun og grafið fyrir f(x) = x², en því hefur verið hliðrað 6 einingar til hægri og 10 einingar upp. Topppunktur þess er í (6, 10).

Grafið sem táknar f(x) = x² er hliðrað 2 einingar til vinstri og 10 einingar niður og speglað þannig að það opnast niður, eins og sýnt er.

A coordinate plane displays a graph of the parent quadratic function in blue. Another parabola, graphed in black, was transformed using the parameters in the question. The x-axis extends from negative 6 to positive 6 with a scale of 2 while the y-axis extends from negative 30 to positive 30 with a scale of 10.

Hvaða jafna skilgreinir þennan feril?

Lausn

$//www.w3.org/1998/Math/MathML" display="block" alttext="f(x) = −(x + 2)² − 10"> f (x) = - {(x + 2)}^{2} - 10$
$//www.w3.org/1998/Math/MathML" display="block" alttext="f(x) = (x + 2)² − 10"> f (x) = {(x + 2)}^{2} - 10$
$//www.w3.org/1998/Math/MathML" display="block" alttext="f(x) = −(x + 2)² + 10"> f (x) = - {(x + 2)}^{2} + 10$
//www.w3.org/1998/Math/MathML" display="block" alttext="f(x) = (x + 2)² + 10">
f(x)=(x+2)2+10
Svar:
$f(x) = −(x + 2)² − 10$
FYRRI KAFLI
7.17.4 Umbreyting grunnfallsins
NÆSTI KAFLI
7.17.6 Æfingar
Leita í bók...
Algebra 1 (IS)
Um þetta námskeið
Flýtibyrjun
Notkun Desmos
Ítarefni
1.15.0 Yfirlit kennslustundar
1.15.1 Að leysa hlutföll
1.15.2 Líkanagerð jafna með beinu hlutfalli
1.15.3 Að nota beint hlutfall til að leysa hagnýt verkefni, hluti 1
1.15.4 Að nota beint hlutfall til að leysa hagnýt verkefni, hluti 2
1.15.5 Æfingar
1.15.6 Samantekt kennslustundar
1.5.0 Yfirlit kennslustundar
1.5.1 Greining á gröfum línulegra jafna
1.5.2 Teikning línulegra falla með tveimur breytum
1.5.3 Að skoða jöfnu með tveimur breytum og graf hennar, hluti 1
1.5.4 Ritun, teikning og lausn línulegrar jöfnu
1.5.5 Að skoða jöfnu með tveimur breytum og graf hennar, hluti 2
1.5.6 Æfingar
1.5.7 Samantekt kennslustundar
1.3.0 Yfirlit kennslustundar
1.3.1 Að finna tengsl milli 𝑥 og 𝑦
1.3.2 Að lýsa tengslum með orðum og jöfnum
1.3.3 Að greina og tákna tengsl
1.3.4 Að rita jöfnu til að tákna tengsl
1.3.5 Æfingar
1.3.6 Samantekt kennslustundar
1.4.0 Yfirlit kennslustundar
1.4.1 Að finna lausn á jöfnu með einni breytu, hluti 1
1.4.2 Að rita jöfnur til að tákna skorður
1.4.3 Að finna lausn á jöfnu með tveimur breytum
1.4.4 Að finna lausn á jöfnu með einni breytu, hluti 2
1.4.5 Æfingar
1.4.6 Samantekt kennslustundar
1.7.0 Yfirlit kennslustundar
1.7.1 Að ákvarða hvort núll sé lausn
1.7.2 Að útskýra leyfilegar aðgerðir til að leysa jöfnu
1.7.3 Að skilja jöfnur með enga lausn eða óendanlega margar lausnir
1.7.4 Að leysa jöfnur með deilingu
1.7.5 Æfingar
1.7.6 Samantekt kennslustundar
1.9.0 Yfirlit kennslustundar
1.9.1 Að umrita jöfnu með þremur breytum
1.9.2 Að skrifa jöfnu til að tákna skorðu
1.9.3 Að skrifa og umrita jöfnur með tveimur breytum
1.9.4 Að leysa fyrir tiltekna breytu
1.9.5 Æfingar
1.9.6 Samantekt kennslustundar
1.10.0 Yfirlit kennslustundar
1.10.1 Að túlka jöfnur í samhengi
1.10.2 Að teikna gröf jafna í samhengi
1.10.3 Að skrifa jöfnur á staðalformi og teikna gröf þeirra
1.10.4 Að para saman jöfnur og gröf
1.10.5 Æfingar
1.10.6 Samantekt kennslustundar
1.11.0 Yfirlit kennslustundar
1.11.1 Að beita dreifireglu til að umrita stæður
1.11.2 Að tengja jöfnur með tveimur breytum, gröf þeirra og aðstæður
1.11.3 Að beita táknrænni og óhlutbundinni röksemdafærslu um línulegar jöfnur
1.11.4 Að bera kennsl á eiginleika grafs
1.11.5 Æfingar
1.11.6 Samantekt kennslustundar
1.12.0 Yfirlit kennslustundar
1.12.1 Að nota formúlu fyrir hallatölu
1.12.2 Að skrifa jöfnu út frá hallatölu og skurðpunkti við y-ás
1.12.3 Að skrifa jöfnu út frá hallatölu og punkti
1.12.4 Að skrifa jöfnur á mismunandi formum
1.12.5 Að skrifa jöfnu út frá tveimur punktum
1.12.6 Að velja aðferð til að skrifa jöfnu
1.12.7 Æfingar
1.12.8 Samantekt kennslustundar
1.13.0 Yfirlit kennslustundar
1.13.1 Að skrifa línulegar jöfnur
1.13.2 Að búa til töflur út frá lýsingum með orðum
1.13.3 Að para saman töflur, jöfnur og gröf
1.13.4 Að búa til töflu út frá jöfnu
1.13.5 Æfingar
1.13.6 Samantekt kennslustundar
1. hluti: Samantekt
1.8.0 Yfirlit kennslustundar
1.8.1 Að lýsa tengslum milli tveggja stærða
1.8.2 Að velja gagnlegasta form jöfnu
1.8.3 Að skrifa jöfnur og einangra breytur
1.8.4 Að skrifa jöfnur út frá málum forma
1.8.5 Æfingar
1.8.6 Samantekt kennslustundar
1.1.0 Yfirlit kennslustundar
1.1.1 Skilningur á gildi
1.1.2 Búa til stæður til að áætla kostnað, hluti 1
1.1.3 Skilningur á skorðum
1.1.4 Búa til stæður til að áætla kostnað, hluti 2
1.1.5 Æfing
1.1.6 Samantekt kennslustundar
1.2.0 Yfirlit kennslustundar
1.2.1 Að finna prósentu af 200
1.2.2 Líkanagerð með jöfnum til að finna brúnir platónskra margflötunga
1.2.3 Ritun jafna til að tákna tengsl
1.2.4 Ritun jafna til að tákna tengsl með prósentum
1.2.5 Að rita jöfnur fyrir stuttermabolapöntun
1.2.6 Æfingar
1.2.7 Samantekt kennslustundar
Yfirlit yfir 1. hluta
Stutt upprifjun: að leysa línulegar jöfnur
Stutt upprifjun: að flokka jöfnur
Finna hnit: Smákennsla upprifjun
Yfirlit yfir 1. hluta: samantekt
Námsráð
Að skapa þitt besta sjálf
Að byggja upp tengsl
1.14.0 Yfirlit kennslustundar
1.14.1 Notkun punkthallaforms til að rita jöfnu línu
1.14.2 Ritun jafna á punkthallaformi og hallatöluformi
1.14.3 Að skrifa jöfnu línu sem er samsíða gefinni línu
1.14.4 Að skrifa jöfnu línu sem er hornrétt á gefna línu
1.14.5 Að skrifa jöfnu línu sem er samsíða eða hornrétt á ás
1.14.6 Að teikna samsíða og hornréttar línur
1.14.7 Æfingar
1.14.8 Samantekt kennslustundar
1.6.0 Yfirlit kennslustundar
1.6.1 Að kanna jafngildar stæður
1.6.2 Að setja tengsl fram sem jöfnur
1.6.3 Könnun á skyldum jöfnum
1.6.4 Að bera kennsl á skyldar jöfnur
1.6.5 Æfingar
1.6.6 Samantekt kennslustundar
Verkefni 1 Yfirlit
Taka eftir og velta fyrir sér: einkenni grafs
Pörun grafa og jafna
2.14.0 Yfirlit kennslustundar
2.14.1 Að setja upp jöfnur til að leysa gátu
2.14.2 Að finna tvennd gilda sem uppfyllir margar ójöfnur
2.14.3 Að skrifa ójöfnuhneppi sem tákna aðstæður
2.14.4 Að teikna lausnamengi ójöfnuhneppa
2.14.5 Að skrifa ójöfnur fyrir aðstæður og sýna þær á grafi
2.14.6 Æfingar
2.14.7 Samantekt kennslustundar
2.1.0 Yfirlit kennslustundar
2.1.1 Að skilja skorður og gildi
2.1.2 Að skrifa og teikna jöfnur
2.1.3 Að uppfylla skorður
2.1.4 Að kanna jöfnuhneppi
2.1.5 Æfingar
2.1.6 Samantekt kennslustundar
2.2.0 Yfirlit kennslustundar
2.2.1 Túlkun á gröfum jöfnuhneppa
2.2.2 Að skrifa jöfnuhneppi út frá töflum
2.2.3 Gröf jöfnuhneppa
2.2.4 Jöfnuhneppi í raunverulegum aðstæðum
2.2.5 Æfingar
2.2.6 Samantekt kennslustundar
2.5.0 Yfirlit kennslustundar
2.5.1 Að skrifa og prófa nýjar jöfnur
2.5.2 Að leggja saman tvær jöfnur í jöfnuhneppi
2.5.3 Að leysa línuleg jöfnuhneppi með tveimur breytum
2.5.4 Að leysa jöfnuhneppi með raunverulegum dæmum
2.5.5 Æfingar
2.5.6 Samantekt kennslustundar
2.6.0 Yfirlit kennslustundar
2.6.1 Að margfalda jöfnur með tölu
2.6.2 Að skrifa nýtt jöfnuhneppi til að leysa gefið jöfnuhneppi
2.6.3 Að finna lausnir í óröðuðum söfnum jafngildra jöfnuhneppa
2.6.4 Að búa til jafngild jöfnuhneppi
2.6.5 Æfingar
2.6.6 Samantekt kennslustundar
2.7.0 Yfirlit kennslustundar
2.7.1 Línuleg jöfnuhneppi með óendanlega mörgum lausnum
2.7.2 Línuleg jöfnuhneppi sem hafa enga lausn
2.7.3 Að flokka jöfnuhneppi eftir fjölda lausna
2.7.4 Að skrifa samkvæm og ósamkvæm jöfnuhneppi
2.7.5 Æfingar
2.7.6 Samantekt kennslustundar
2.8.0 Yfirlit kennslustundar
2.8.1 Að skilja ójöfnutákn
2.8.2 Að greina skorður í ójöfnum
2.8.3 Að skrifa ójöfnur sem tákna skorður
2.8.4 Að skrifa fleiri ójöfnur
2.8.5 Æfingar
2.8.6 Samantekt kennslustundar
2.9.0 Yfirlit kennslustundar
2.9.1 Að skrá lausnir ójafna
2.9.2 Að sýna lausnir ójafna á talnalínu
2.9.3 Að skilja merkingu ójöfnu
2.9.4 Að átta sig á ójöfnum og lausnum þeirra
2.9.5 Að bera saman jöfnur og ójöfnur
2.9.6 Að nota tækni til að skoða lausnir ójafna myndrænt
2.9.7 Að finna lausnir ójafna á talnalínu
2.9.8 Æfingar
2.9.9 Samantekt kennslustundar
2.10.0 Yfirlit kennslustundar
2.10.1 Að skrifa ójöfnu sem táknar skorðu
2.10.2 Að nota ójöfnur til að leysa verkefni
2.10.3 Mismunandi leiðir til að leysa ójöfnu
2.10.4 Að para saman ójöfnur og lausnir
2.10.5 Að leysa ójöfnur
2.10.6 Að skrifa ójöfnur sem tákna aðstæður
2.10.7 Æfingar
2.10.8 Samantekt kennslustundar
2.11.0 Yfirlit kennslustundar
2.11.1 Að nota útreikninga og röksemdafærslu
2.11.2 Að finna lausnir ójafna í hnitakerfi
2.11.3 Að teikna lausnamengi ójafna
2.11.4 Að skyggja svæði við markalínu
2.11.5 Æfingar
2.11.6 Samantekt kennslustundar
2.12.0 Yfirlit kennslustundar
2.12.1 Að teikna graf sem táknar jöfnu
2.12.2 Að skrifa ójöfnu sem táknar skorðu
2.12.3 Að teikna lausnamengi og túlka punkta
2.12.4 Að greina punkta á markalínu
2.12.5 Að ákvarða hvort punktar séu lausnir ójöfnu
2.12.6 Æfingar
2.12.7 Samantekt kennslustundar
2.13.0 Yfirlit kennslustundar
2.13.1 Að teikna lausnamengi ójafna með grafreiknitæki
2.13.2 Að leysa verkefni með ójöfnum með tveimur breytum
2.13.3 Að para saman framsetningar ójafna
2.13.4 Að leysa verkefni með ójöfnum með töflum
2.13.5 Að teikna lausnamengi ójöfnu
2.13.6 Æfingar
2.13.7 Samantekt kennslustundar
Yfirlit verkefnis 2
Að ákvarða lausn ójafna
Að túlka safn stærðfræðilíkana
Að vinna stærðfræðilega líkanagerð
Samantekt 2. hluta
2. hluti Yfirlit
Að ákvarða röðuðu tvenndina: upprifjun smákennslu
Að finna hallatölu og skurðpunkt við y-ás: upprifjun smákennslu
Að finna skurðpunkta við x-ás og y-ás: upprifjun smákennslu
2. hluti: Samantekt á yfirliti
2.3.0 Yfirlit kennslustundar
2.3.1 Að finna tengsl milli grafa og jafna
2.3.2 Að athuga lausnir jöfnuhneppa
2.3.3 Að leysa jöfnur með innsetningaraðferðinni
2.3.4 Að leysa fleiri jöfnur
2.3.5 Æfingar
2.3.6 Samantekt kennslustundar
2.4.0 Yfirlit kennslustundar
2.4.1 Að sameina tvær sannar jöfnur
2.4.2 Að leggja saman jöfnur
2.4.3 Að leggja saman og draga frá jöfnuhneppi og nota gröf þeirra
2.4.4 Að velja bestu aðferðina til að leysa jöfnuhneppi
2.4.5 Æfingar
2.4.6 Samantekt kennslustundar
2.15.0 Yfirlit kennslustundar
2.15.1 Að greina gröf sem tákna línulegar jöfnur og ójöfnur
2.15.2 Að ákvarða hvort punktar á markalínum séu lausnir hneppis
2.15.3 Að leysa verkefni með mörgum skorðum samtímis
2.15.4 Að finna hvaða svæði grafs tilheyra lausn hneppis
2.15.5 Æfingar
2.15.6 Samantekt kennslustundar
Yfirlit yfir verkefni 3
Að áætla lengdir
Að greina gögn
Yfirlit 3. hluta
Að greina mynstur: Upprifjun smákennslu
Að greina jákvæða og neikvæða leitni: Upprifjun smákennslu
Að túlka hallatölu og skurðpunkt við y-ás: Upprifjun smákennslu
Samantekt yfirlits 3. hluta
3.2.0 Yfirlit kennslustundar
3.2.1 Að velja bestu línuna
3.2.2 Að finna línu sem fellur best að gögnunum
3.2.3 Að skrifa línuleg líkön án tæknibúnaðar
3.2.4 Að meta hversu vel línulegt líkan fellur að gögnum
3.2.5 Að vinna með línur sem falla að gögnum
3.2.6 Æfingar
3.2.7 Samantekt kennslustundar
3.3.0 Yfirlit kennslustundar
3.3.1 Að draga áætlað gildi frá raungildi
3.3.2 Að teikna og greina leifar
3.3.3 Að para saman leifarit og dreifirit
3.3.4 Að finna línu sem fellur best að gögnum út frá leifariti
3.3.5 Æfingar
3.3.6 Samantekt kennslustundar
3.4.0 Yfirlit kennslustundar
3.4.1 Að bera saman dreifirit með línulegri og ólínulegri leitni
3.4.2 Greining mismunar á punktaritum
3.4.3 Að finna fylgnistuðul með tæknibúnaði
3.4.4 Pörun fylgnistuðla
3.4.5 Að nota fylgnistuðul til að meta línu sem fellur að gögnum
3.4.6 Æfing
3.4.7 Samantekt kennslustundar
3.5.0 Yfirlit kennslustundar
3.5.1 Að nota tvíbreytugögn í samhengi
3.5.2 Að finna og nota fylgnistuðul til að túlka styrk línulegs sambands
3.5.3 Að nota fylgnistuðul til að lýsa sambandi tveggja breyta
3.5.4 Að túlka fylgnistuðul
3.5.5 Æfingar
3.5.6 Samantekt kennslustundar
3.6.0 Yfirlit kennslustundar
3.6.1 Að lýsa sambandi milli breyta
3.6.2 Að lýsa hvernig tvær breytur tengjast
3.6.3 Að nota hugtakið orsakasamband
3.6.4 Að ákvarða tegund sambands
3.6.5 Æfingar
3.6.6 Samantekt kennslustundar
Lokaorð 3. hluta
3.1.0 Yfirlit kennslustundar
3.1.1 Að kanna dreifirit
3.1.2 Að búa til dreifirit út frá gögnum
3.1.3 Að túlka hallatölu og skurðpunkt við y-ás í línulegu líkani
3.1.4 Að túlka hallatölu og skurðpunkt við y-ás í dreifiriti
3.1.5 Að nota jöfnu línu sem fellur vel að gögnum
3.1.6 Æfingar
3.1.7 Samantekt kennslustundar
Yfirlit yfir rannsóknarverkefni
Hermun sambanda
Hvað er fall?
Mismunandi tegundir falla
Yfirlit 4. hluta
Finna hallatölu: Upprifjun
Lýsa gröfum: Upprifjun
Framlengja mynstur: Upprifjun
Yfirlit 4. hluta: Lokaorð
4.1.0 Yfirlit kennslustundar
4.1.1 Samanburður tveggja sambanda með röksemdafærslu
4.1.2 Myndræn röksemdafærsla um samband tveggja stærða
4.1.3 Skoðun vensla og falla
4.1.4 Lýsing á fallssamböndum
4.1.5 Að setja tengsl tveggja breyta fram með líkani
4.1.6 Æfing
4.1.7 Samantekt kennslustundar
4.2.0 Yfirlit kennslustundar
4.2.1 Að túlka gröf til að svara spurningum
4.2.2 Túlkun fullyrðinga á rithætti falla
4.2.3 Að finna nákvæmlega eitt úttak fyrir hvert inntak
4.2.4 Að skilja falltáknun með hagnýtum verkefnum
4.2.5 Æfingar
4.2.6 Samantekt kennslustundar
4.3.0 Yfirlit kennslustundar
4.3.1 Að bera saman fallgildi
4.3.2 Að rita staðhæfingar út frá falltáknun
4.3.3 Að bera saman staðhæfingar í falltáknun
4.3.4 Að nota falltáknun í raunverulegu dæmi
4.3.5 Æfingar
4.3.6 Samantekt kennslustundar
4.4.0 Yfirlit kennslustundar
4.4.1 Að nota falltáknun í gildistöflum
4.4.2 Að skilgreina föll með reglu
4.4.3 Að nota töflur til að finna fallreglur
4.4.4 Að rita reglu með falltáknun
4.4.5 Æfingar
4.4.6 Samantekt kennslustundar
4.6.0 Yfirlit kennslustundar
4.6.1 Að túlka staðhæfingar í falltáknun
4.6.2 Að greina gröf falla
4.6.3 Að tengja saman graf og orðalýsingu á falli
4.6.4 Helstu eiginleikar línulegra falla
4.6.5 Að túlka gröf
4.6.6 Æfingar
4.6.7 Samantekt kennslustundar
4.7.0 Yfirlit kennslustundar
4.7.1 Að reikna gildi brota
4.7.2 Að finna hallatölu út frá töflum, gröfum og punktum
4.7.3 Að rita línulegar jöfnur
4.7.4 Að rita jöfnur út frá tveimur punktum
4.7.5 Æfingar
4.7.6 Samantekt kennslustundar
4.8.0 Yfirlit kennslustundar
4.8.1 Að bera saman breytingar á úttaki út frá inntaki
4.8.2 Meðalbreytingarhraði og hallatala
4.8.3 Meðalbreytingarhraði fundinn og túlkaður
4.8.4 Breytingarhraði línulegra falla
4.8.5 Að túlka meðalbreytingarhraða með dæmum úr raunveruleikanum
4.8.6 Æfingar
4.8.7 Samantekt kennslustundar
4.9.0 Yfirlit kennslustundar
4.9.1 Að greina og bera saman eiginleika grafa
4.9.2 Að túlka gröf án mælieininga
4.9.3 Að teikna drög að gröfum falla
4.9.4 Framsetning stærða í tilteknum aðstæðum
4.9.5 Að nota orðalýsingar til að búa til gröf falla
4.9.6 Æfingar
4.9.7 Samantekt kennslustundar
4.10.0 Yfirlit kennslustundar
4.10.1 Að greina gröf og staðhæfingar í falltáknun
4.10.2 Að túlka gröf og staðhæfingar út frá aðstæðum
4.10.3 Samanburður falla sem sett eru fram á aðskildum gröfum
4.10.4 Að bera saman gröf og staðhæfingar sem tákna föll án samhengis
4.10.5 Að greina föll í raunverulegu samhengi
4.10.6 Æfingar
4.10.7 Samantekt kennslustundar
4.11.0 Yfirlit kennslustundar
4.11.1 Að teikna gröf línulegra falla
4.11.2 Lóðréttar hliðranir
4.11.3 Láréttar hliðranir
4.11.4 Lóðréttar teygjur og samþjöppun
4.11.5 Láréttar teygjur og samþjöppun
4.11.6 Að teikna gröf með umbreytingum
4.11.7 Æfingar
4.11.8 Samantekt kennslustundar
4.12.0 Yfirlit kennslustundar
4.12.1 Að ákvarða skynsamleg inntaks- og úttaksgildi
4.12.2 Formengi: inntak falls
4.12.3 Myndmengi: úttak falls
4.12.4 Notkun grafa til að ákvarða formengi falls
4.12.5 Að nota föll til að svara spurningum úr raunveruleikanum
4.12.6 Æfingar
4.12.7 Samantekt kennslustundar
4.13.0 Yfirlit kennslustundar
4.13.1 Mismunandi eiginleikar grafs
4.13.2 Gröf falla
4.13.3 Að finna formengi og myndmengi út frá grafi
4.13.4 Formengi og myndmengi í raunveruleikanum
4.13.5 Graf falls og tengsl formengis og myndmengis
4.13.6 Æfingar
4.13.7 Samantekt kennslustundar
4.14.0 Yfirlit kennslustundar
4.14.1 Lýstu mynstrinu
4.14.2 Hvað er runa?
4.14.3 Tengslin milli runa og liða
4.14.4 Reglur fyrir runu
4.14.5 Æfingar
4.14.6 Samantekt kennslustundar
4.15.0 Yfirlit kennslustundar
4.15.1 Hver eru mynstrin?
4.15.2 Notkun taflna og grafa til að setja fram kvótarunur
4.15.3 Ljúktu við rununa
4.15.4 Tengsl kvótans og liðar í runu
4.15.5 Æfingar
4.15.6 Samantekt kennslustundar
4.16.0 Yfirlit kennslustundar
4.16.1 Að túlka falltáknun
4.16.2 Hvað er jafnmunaruna?
4.16.3 Runa er tegund falls
4.16.4 Að þekkja og mynda runur
4.16.5 Æfingar
4.16.6 Samantekt kennslustundar
4.17.0 Yfirlit kennslustundar
4.17.1 Að skilgreina runu
4.17.2 Hvað er rakningarregla?
4.17.3 Leiðir til að setja fram runu
4.17.4 Rakningarreglur fyrir kvótarunur
4.17.5 Æfingar
4.17.6 Samantekt kennslustundar
4.18.0 Yfirlit kennslustundar
4.18.1 Endurteknar aðgerðir
4.18.2 Að greina formengi falls
4.18.3 Skilgreina jafnmunarunu með n-ta liðnum
4.18.4 Skilgreina kvótarunu með n-ta liðnum
4.18.5 Að skipta á milli formúla
4.18.6 Mismunandi tegundir jafna
4.18.7 Æfingar
4.18.8 Samantekt kennslustundar
Yfirlit verkefnis 4
Áætla hleðslutíma rafhlöðu
Greina hleðsluprósentu yfir tíma
Skrifa jöfnu til að gera líkan af gögnum
Samantekt 4. hluta
4.5.0 Yfirlit kennslustundar
4.5.1 Að finna lausnir jafna
4.5.2 Að nota lóðrétta línuprófið
4.5.3 Samanburður falla
4.5.4 Að nota falltáknun og grafreiknivél
4.5.5 Að finna óþekktar stærðir í línulegum föllum með myndrænni og algebrulegri aðferð
4.5.6 Æfingar
4.5.7 Samantekt kennslustundar
5.7.0 Yfirlit kennslustundar
5.7.1 Mynstur í rauntölum
5.7.2 Að bera saman gröf
5.7.3 Að lýsa gröfum
5.7.4 Stærðir sem breytast samkvæmt vísisfalli
5.7.5 Æfingar
5.7.6 Samantekt kennslustundar
Yfirlit 5. hluta
Ritun línulegra falla út frá grafi: Upprifjun
Túlkun línulegra falla: Upprifjun
Reikna gildi veldisstæðna: Upprifjun
Yfirlit 5. hluta: Samantekt
5.1.0 Yfirlit kennslustundar
5.1.1 Skilningur á veldum
5.1.2 Notkun margfeldis- og kvótareglna fyrir veldi
5.1.3 Notkun núllveldisreglu og neikvæðra velda
5.1.4 Veldisreglur fyrir veldi
5.1.5 Einföldun velda
5.1.6 Æfingar
5.1.7 Samantekt kennslustundar
5.2.0 Yfirlit kennslustundar
5.2.1 Ferningstölur rifjaðar upp
5.2.2 n-ta rótin
5.2.3 Rótarstæður og ræðir veldisvísar
5.2.4 Veldisreglur með ræðum veldisvísum
5.2.5 Æfingar
5.2.6 Samantekt kennslustundar
5.3.0 Yfirlit kennslustundar
5.3.1 Myndræn framsetning á veldisvexti
5.3.2 Könnun á mismunandi vaxtarmynstrum
5.3.3 Samanburður á tveimur mynstrum
5.3.4 Að tengja stæður og töflur við aðstæður
5.3.5 Að lýsa breytingum á vexti stærðfræðilega
5.3.6 Æfingar
5.3.7 Samantekt kennslustundar
5.4.0 Yfirlit kennslustundar
5.4.1 Veldisreglur
5.4.2 Núllveldisreglan
5.4.3 Veldisbreyting: vaxtarstuðullinn
5.4.4 Að teikna gröf veldisstæðna
5.4.5 Að túlka vaxtarstuðul jöfnu
5.4.6 Æfingar
5.4.7 Samantekt kennslustundar
5.5.0 Yfirlit kennslustundar
5.5.1 Að bera kennsl á línulegar stærðir og stærðir sem breytast veldislega
5.5.2 Vísishnignun
5.5.3 Að nota gröf til að sýna vísishnignun
5.5.4 Að rökstyðja veldislíkön
5.5.5 Að skrifa jöfnur sem lýsa vísishnignun
5.5.6 Æfingar
5.5.7 Samantekt kennslustundar
5.6.0 Yfirlit kennslustundar
5.6.1 Athugun á veldisreglum
5.6.2 Að túlka neikvæða veldisvísa í veldisvexti
5.6.3 Að túlka neikvæða veldisvísa í vísishnignun
5.6.4 Staðalform
5.6.5 Að nota staðalform
5.6.6 Að túlka neikvæða veldisvísa og staðalform
5.6.7 Æfingar
5.6.8 Samantekt kennslustundar
5.8.0 Yfirlit kennslustundar
5.8.1 Merking falls sem sett er fram myndrænt
5.8.2 Framsetning falls sem gildistafla, graf og jafna
5.8.3 Mál falla og falltáknun
5.8.4 Falltáknun
5.8.5 Æfingar
5.8.6 Samantekt kennslustundar
5.9.0 Yfirlit kennslustundar
5.9.1 Reikna gildi stæðna fyrir mismunandi gildi á x
5.9.2 Greina undirliggjandi tengsl í grafi falls
5.9.3 Teikna gröf jafna til að leysa verkefni
5.9.4 Að velja grafglugga
5.9.5 Túlka gröf til að finna nálguð gildi
5.9.6 Æfingar
5.9.7 Samantekt kennslustundar
5.10.0 Yfirlit kennslustundar
5.10.1 Reikna meðalbreytingarhraða út frá tveimur punktum
5.10.2 Kanna meðalbreytingarhraða í veldisvexti
5.10.3 Kanna meðalbreytingarhraða í vísishnignun
5.10.4 Meðalbreytingarhraði
5.10.5 Æfingar
5.10.6 Samantekt kennslustundar
5.11.0 Yfirlit kennslustundar
5.11.1 Að breyta grafglugga
5.11.2 Velja viðeigandi líkan
5.11.3 Líkanagerð með vísisföllum
5.11.4 Skoða vísishnignun í samhengi
5.11.5 Nota líkön af tengslum til að svara spurningum
5.11.6 Æfingar
5.11.7 Samantekt kennslustundar
5.12.0 Yfirlit kennslustundar
5.12.1 Líkanagerð með vísishnignun
5.12.2 Jöfnur og gröf þeirra
5.12.3 Gröf sem tákna vísishnignun
5.12.4 Möguleg jafna falls út frá grafi
5.12.5 Æfingar
5.12.6 Samantekt kennslustundar
5.13.0 Yfirlit kennslustundar
5.13.1 Samanburður falla
5.13.2 Að búa til vísisföll út frá gröfum
5.13.3 Samanburður vísisfalla
5.13.4 Að túlka eiginleika grafs vísisfalls
5.13.5 Æfingar
5.13.6 Samantekt kennslustundar
5.14.0 Yfirlit kennslustundar
5.14.1 Að greina línulegan vöxt frá veldisvexti
5.14.2 Að nota töflur til að bera saman línuleg föll og vísisföll
5.14.3 Samanburður línulegra falla og vísisfalla
5.14.4 Að nota falltáknun til að bera saman línuleg föll og vísisföll
5.14.5 Æfingar
5.14.6 Samantekt kennslustundar
5.15.0 Yfirlit kennslustundar
5.15.1 Að rita jafngildar stæður
5.15.2 Fastur breytingarhraði línulegs falls
5.15.3 Vaxtarhraði vísisfalls
5.15.4 Samanburður á línulegum vexti og veldisvexti
5.15.5 Æfingar
5.15.6 Samantekt kennslustundar
Yfirlit verkefnis 5
Greining gagna
Að rita jöfnur fyrir mannfjöldalíkön
Opin líkanagerð með gagnarannsókn
Samantekt á kafla 5
Yfirlit kafla 6
Einföldun stæðna með reglum um veldi: Upprifjun
Einföldun stæðna með dreifireglunni: Upprifjun
Að finna stærsta samdeili: Upprifjun
Yfirlit kafla 6: Samantekt
Yfirlit rannsóknarverkefnis
Að uppgötva flatarmálslíkan
Að skilja flatarmálslíkan
Að nota flatarmálslíkan
Að beita flatarmálslíkani á margliður
6.1.0 Yfirlit kennslustundar
6.1.1 Að skilja margliður
6.1.2 Að leggja saman og draga frá margliður
6.1.3 Að reikna gildi margliðufalls fyrir gefið gildi
6.1.4 Að leggja saman og draga frá margliðuföll
6.1.5 Upprifjun á samlagningu og frádrætti margliða
6.1.6 Æfingar
6.1.7 Samantekt kennslustundar
6.2.0 Yfirlit kennslustundar
6.2.1 Margföldun einliða
6.2.2 Margföldun tvíliða
6.2.3 Margföldun margliðu með margliðu
6.2.4 Margföldun sérstakra margfelda
6.2.5 Margföldun margliðufalla
6.2.6 Æfingar
6.2.7 Samantekt kennslustundar
6.3.0 Yfirlit kennslustundar
6.3.1 Deiling með einliðum
6.3.2 Deiling margliða með langdeilingu
6.3.3 Deiling margliða með reikniriti Horners
6.3.4 Deiling margliðufalla og afgangssetningin
6.3.5 Að nota þáttasetninguna
6.3.6 Æfingar
6.3.7 Samantekt kennslustundar
6.4.0 Yfirlit kennslustundar
6.4.1 Að finna þætti
6.4.2 Að finna stærsta samdeili tveggja eða fleiri stæðna
6.4.3 Að taka stærsta samdeili út fyrir sviga í margliðum
6.4.4 Að þátta margliður með hópun
6.4.5 Er hægt að þátta margliðuna?
6.4.6 Æfingar
6.4.7 Samantekt kennslustundar
6.5.0 Yfirlit kennslustundar
6.5.1 Að snúa FOIL-aðferðinni við
6.5.2 Þáttun þríliða þar sem forystustuðullinn er 1
6.5.3 Þáttun þríliða með því að prófa sig áfram
6.5.4 Þáttun þríliða með ac-aðferðinni og innsetningu
6.5.5 Að velja eigin aðferð til að þátta þríliði
6.5.6 Æfingar
6.5.7 Samantekt kennslustundar
6.6.0 Yfirlit kennslustundar
6.6.1 Að bera kennsl á þríliði sem eru ferningar tvíliða
6.6.2 Þáttun þríliða sem eru ferningar tvíliða
6.6.3 Þáttun mismunar tveggja ferninga
6.6.4 Að flokka margliður eftir þáttunaraðferðum
6.6.5 Æfingar
6.6.6 Samantekt kennslustundar
6.7.0 Yfirlit kennslustundar
6.7.1 Þáttunaraðferðir fyrir margliður
6.7.2 Upprifjun á almennum aðferðum við þáttun margliðu
6.7.3 Beiting almennra aðferða við þáttun
6.7.4 Er margliðan fullþáttuð?
6.7.5 Æfingar
6.7.6 Samantekt kennslustundar
Yfirlit verkefnis 6
Flatarmál rétthyrninga
Mál og flatarmál rétthyrninga
Búðu til þína eigin rétthyrninga
Samantekt á kafla 6
Yfirlit 7. hluta
Margföldun tvíliða: stutt upprifjun
Þáttun þríliða: stutt upprifjun
Samanburður línulegra falla og vísisfalla: stutt upprifjun
Yfirlit kafla 7: samantekt
7.1.0 Yfirlit kennslustundar
7.1.1 Að koma auga á ný breytingamynstur
7.1.2 Tengsl lengdar og flatarmáls
7.1.3 Mælingar færðar í hnitakerfi
7.1.4 Inntak og úttak falls
7.1.5 Æfingar
7.1.6 Samantekt kennslustundar
7.2.0 Yfirlit kennslustundar
7.2.1 Ferningar í rúmfræðilegu mynstri
7.2.2 Jöfn breyting og veldisbreyting
7.2.3 Annars stigs stæður
7.2.4 Annars stigs tengsl
7.2.5 Æfingar
7.2.6 Samantekt kennslustundar
7.3.0 Yfirlit kennslustundar
7.3.1 Annars stigs stæður og flatarmál
7.3.2 Jöfnur ritaðar fyrir mynstur með ferningum
7.3.3 Annars stigs runur
7.3.4 Er mynstrið annars stigs fall?
7.3.5 Æfingar
7.3.6 Samantekt kennslustundar
7.4.0 Yfirlit kennslustundar
7.4.1 Samanburður stæðna
7.4.2 Línulegur vöxtur, veldisvöxtur og annars stigs vöxtur
7.4.3 Samanburður vísisfalla og annars stigs falla
7.4.4 Samanburður stæðna með veldisvísum og annars stigs stæðna
7.4.5 Æfingar
7.4.6 Samantekt kennslustundar
7.5.0 Yfirlit kennslustundar
7.5.1 Talnamynstur
7.5.2 Annars stigs líkan fyrir tengsl tíma og vegalengdar
7.5.3 Vegalengd sem annars stigs fall af liðnum tíma
7.5.4 Annars stigs stæða sem lýsir tengslum vegalengdar og tíma
7.5.5 Æfingar
7.5.6 Samantekt kennslustundar
7.6.0 Yfirlit kennslustundar
7.6.1 Að nota línuleg föll til að lýsa jöfnum hraða
7.6.2 Áhrif þyngdarafls á annars stigs föll
7.6.3 Að nota annars stigs föll til að lýsa hæð
7.6.4 Að túlka gröf annars stigs falla
7.6.5 Æfingar
7.6.6 Samantekt kennslustundar
7.7.0 Yfirlit kennslustundar
7.7.1 Samanburður á gröfum falla
7.7.2 Líkanagerð með raunverulegum gögnum og annars stigs föllum
7.7.3 Skilgreiningarmengi, topppunktur og núllstöð annars stigs falla
7.7.4 Tengsl skilgreiningarmengis falls við graf þess
7.7.5 Æfingar
7.7.6 Samantekt kennslustundar
7.8.0 Yfirlit kennslustundar
7.8.1 Flatarmálsmyndir
7.8.2 Dreifireglan notuð til að rita jafngildar stæður
7.8.3 Skýringarmyndir notaðar til að finna jafngildar annars stigs stæður
7.8.4 Að rita jafngildar stæður
7.8.5 Æfingar
7.8.6 Samantekt kennslustundar
7.9.0 Yfirlit kennslustundar
7.9.1 Að leysa jöfnur með andhverfum aðgerðum
7.9.2 Að finna margfeldi mismuna
7.9.3 Staðalform og þáttað form annars stigs stæðna
7.9.4 Stæður á staðalformi
7.9.5 Æfingar
7.9.6 Samantekt kennslustundar
7.10.0 Yfirlit kennslustundar
7.10.1 Gröf línulegra jafna
7.10.2 Form annars stigs stæðna og gröf þeirra
7.10.3 Skurðpunktar annars stigs stæðna við x- og y-ás
7.10.4 Að nota staðalform jöfnu til að finna skurðpunkta við x- og y-ás
7.10.5 Æfingar
7.10.6 Samantekt kennslustundar
7.11.0 Yfirlit kennslustundar
7.11.1 Að finna hnit
7.11.2 Þáttað form annars stigs stæðu og skurðpunktar grafs hennar við x-ás
7.11.3 Graf annars stigs falls skissað með að minnsta kosti þremur þekktum punktum
7.11.4 Að nota topppunkt og samhverfuás annars stigs falla
7.11.5 Gröf annars stigs falla
7.11.6 Æfingar
7.11.7 Samantekt kennslustundar
7.12.0 Yfirlit kennslustundar
7.12.1 Að nota stuðla og fastaliði til að bera kennsl á gröf línulegra jafna
7.12.2 Umbreytingar á annars stigs föllum
7.12.3 Að skilja hegðun grafs út frá annars stigs stæðu þess
7.12.4 Framsetningar annars stigs falla
7.12.5 Að bera kennsl á gröf annars stigs falla
7.12.6 Æfingar
7.12.7 Samantekt kennslustundar
7.13.0 Yfirlit kennslustundar
7.13.1 Jafngildar stæður
7.13.2 Línulegi liðurinn í annars stigs stæðu
7.13.3 Að rita jöfnur sem tákna graf
7.13.4 Að rita annars stigs jöfnur út frá rauntölulausnum
7.13.5 Að teikna gröf annars stigs jafna
7.13.6 Æfingar
7.13.7 Samantekt kennslustundar
7.14.0 Yfirlit kennslustundar
7.14.1 Að reikna gildi annars stigs falla í raunverulegu samhengi
7.14.2 Að túlka fallssamband milli tveggja stærða
7.14.3 Að greina föll með mismunandi framsetningum
7.14.4 Að nota annars stigs föll til að leysa verkefni
7.14.5 Að bera kennsl á lykileiginleika falla út frá grafi
7.14.6 Æfingar
7.14.7 Samantekt kennslustundar
7.15.0 Yfirlit kennslustundar
7.15.1 Að greina tvö sett af jöfnum
7.15.2 Topppunktsformið
7.15.3 Hnit topppunktsins
7.15.4 Graf falls á topppunktsformi
7.15.5 Æfingar
7.15.6 Samantekt kennslustundar
7.16.0 Yfirlit kennslustundar
7.16.1 Þrjú form annars stigs stæðna
7.16.2 Að teikna föll á topppunktsformi
7.16.3 Annars stigs jöfnur og gröf
7.16.4 Skissun grafs út frá jöfnu
7.16.5 Æfingar
7.16.6 Samantekt kennslustundar
7.17.0 Yfirlit kennslustundar
7.17.1 Annars stigs stæður á mismunandi formum
7.17.2 Breyting stæðna til að hliðra gröfum
7.17.3 Breyting á stikum annars stigs stæðu
7.17.4 Umbreyting grunnfallsins
7.17.5 Jöfnur grafhliðrana
7.17.6 Æfingar
7.17.7 Samantekt kennslustundar
Yfirlit verkefnis 7
Kynning á hönnun gosbrunns
Hönnun gosbrunns
Samantekt 7. hluta
Yfirlit 8. hluta
Rita jafngildar stæður: Upprifjun úr smákennslu
Finna skurðpunkta við ása: Upprifjun úr smákennslu
Pöra gröf annars stigs falla við jöfnur þeirra: Upprifjun úr smákennslu
Yfirlit 8. hluta: Samantekt
8.1.0 Yfirlit kennslustundar
8.1.1 Skilningur á aðstæðum með annars stigs jöfnum
8.1.2 Gerð líkans fyrir annars stigs vandamál
8.1.3 Setja fram annars stigs jöfnu sem lýsir líkaninu
8.1.4 Túlkun lausnar
8.1.5 Æfing
8.1.6 Samantekt kennslustundar
8.2.0 Yfirlit kennslustundar
8.2.1 Túlkun jafna í samhengi
8.2.2 Kanna aðferðir án grafa til að leysa annars stigs jöfnur
8.2.3 Lausn annars stigs jöfnu sem er sett jöfn núlli
8.2.4 Lausn raunverulegra vandamála með annars stigs jöfnum
8.2.5 Æfing
8.2.6 Samantekt kennslustundar
8.3.0 Yfirlit kennslustundar
8.3.1 Ákvörðun fjölda lausna
8.3.2 Að þekkja lausnapör
8.3.3 Lausn flóknari annars stigs jafna
8.3.4 Að finna lausnirnar
8.3.5 Æfing
8.3.6 Samantekt kennslustundar
8.4.0 Yfirlit kennslustundar
8.4.1 Kynning á núllþáttareglunni
8.4.2 Lausn jafna með vaxandi flækjustigi með röksemdafærslu
8.4.3 Beiting núllþáttareglu til að leysa raunverulegt kastvandamál
8.4.4 Lausn jafna með núllþáttareglu og röksemdafærslu
8.4.5 Æfing
8.4.6 Samantekt kennslustundar
8.5.0 Yfirlit kennslustundar
8.5.1 Upprifjun á núllþáttareglunni
8.5.2 Túlkun grafa til að leysa annars stigs jöfnur
8.5.3 Val á árangursríkri aðferð til að leysa annars stigs jöfnur
8.5.4 Greining villna við lausn annars stigs jafna
8.5.5 Æfing
8.5.6 Samantekt kennslustundar
8.6.0 Yfirlit kennslustundar
8.6.1 Að finna og rökstyðja óþekkta þætti
8.6.2 Notkun skýringarmynda til að skilja jafngildar stæður
8.6.3 Umritun annars stigs stæðna á staðalform
8.6.4 Að finna tölur sem vantar í pör jafngildra stæðna
8.6.5 Æfing
8.6.6 Samantekt kennslustundar
8.7.0 Yfirlit kennslustundar
8.7.1 Skilningur á summum og margfeldum heiltalna
8.7.2 Túlkun neikvæðra fastaliða við þáttun annars stigs stæðna
8.7.3 Greining þátta í 100 og −100
8.7.4 Að finna liði sem vantar
8.7.5 Æfing
8.7.6 Samantekt kennslustundar
8.8.0 Yfirlit kennslustundar
8.8.1 Mat á stæðum með hugarreikningi
8.8.2 Að þekkja liðað margfeldi mismunar tveggja ferninga
8.8.3 Þáttun annars stigs jafna án fyrsta stigs liðar
8.8.4 Ákvörðun um hvort hægt sé að umrita stæðu á þáttað form
8.8.5 Æfing
8.8.6 Samantekt kennslustundar
8.9.0 Yfirlit kennslustundar
8.9.1 Að finna lausn með innsetningu
8.9.2 Notkun þáttaðs forms og núllþáttareglu til að leysa annars stigs jöfnur
8.9.3 Ritun jöfnu sem lýsir annars stigs falli með aðeins eina lausn
8.9.4 Lausn fleiri annars stigs jafna
8.9.5 Æfing
8.9.6 Samantekt kennslustundar
8.10.0 Yfirlit kennslustundar
8.10.1 Greining ýmissa annars stigs stæðna
8.10.2 Vinna með þáttað form annars stigs stæðna með forystustuðul annan en einn
8.10.3 Notkun tækni til að finna ræða þætti
8.10.4 Að finna þætti annars stigs stæðna á staðalformi
8.10.5 Lausn annars stigs jafna með hvaða aðferð sem er
8.10.6 Æfing
8.10.7 Samantekt kennslustundar
8.11.0 Yfirlit kennslustundar
8.11.1 Tengsl annars stigs falls og núllstöðva þess
8.11.2 Að finna annars stigs fall út frá núllstöðvum þess
8.11.3 Að finna annars stigs fall út frá núllstöðvum þess og punkti
8.11.4 Að rita annars stigs föll út frá ólíkum upplýsingum
8.11.5 Æfingar
8.11.6 Samantekt kennslustundar
8.12.0 Yfirlit kennslustundar
8.12.1 Að teikna graf gagnasafns með annars stigs mynstri með tækni
8.12.2 Að finna feril sem fellur best að gögnunum
8.12.3 Að spá fyrir með annars stigs líkani
8.12.4 Að finna gögn sem vantar í safnið
8.12.5 Æfingar
8.12.6 Samantekt kennslustundar
Yfirlit verkefnis 8
Tengsl núllstöðva við þáttað form annars stigs jafna
Umbreyting milli þáttaðs forms og staðalforms
Líkan af flugi eldflaugar með annars stigs jöfnu
Samantekt 8. hluta
9.11.0 Yfirlit kennslustundar
9.11.1 Hágildi og lággildi falls
9.11.2 Táknar topppunkturinn lággildi eða hágildi?
9.11.3 Samanburður á hágildum annars stigs falla
9.11.4 Hágildi, lággildi og greining á topppunkti
9.11.5 Æfingar
9.11.6 Samantekt kennslustundar
Yfirlit 9. hluta
Einfalda rætur: Upprifjun úr smákennslu
Þáttun þríliða sem eru ferningar tvíliða: Upprifjun úr smákennslu
Umbreytingar: Upprifjun úr smákennslu
Yfirlit 9. hluta: Samantekt
9.1.0 Yfirlit kennslustundar
9.1.1 Jöfnur með annars stigs stæðum báðum megin jafnaðarmerkis
9.1.2 Að þekkja uppbyggingu stæðna sem eru ferningar
9.1.3 Að leysa fjölþrepa annars stigs jöfnur með ferningum
9.1.4 Að útskýra hvers vegna stæða er ferningur
9.1.5 Æfingar
9.1.6 Samantekt kennslustundar
9.2.0 Yfirlit kennslustundar
9.2.1 Mismunandi form stæðna sem eru ferningar
9.2.2 Staðalform og þáttað form stæðna sem eru ferningar
9.2.3 Að fylla í ferninginn
9.2.4 Að búa til stæðu sem er ferningur
9.2.5 Æfingar
9.2.6 Samantekt kennslustundar
9.3.0 Yfirlit kennslustundar
9.3.1 Að leysa jöfnur með brotum
9.3.2 Að nota aðferðina að fylla í ferninginn til að leysa jöfnur
9.3.3 Að leysa með því að fylla í ferninginn
9.3.4 Að fylla í ferninginn með brotum
9.3.5 Æfingar
9.3.6 Samantekt kennslustundar
9.4.0 Yfirlit kennslustundar
9.4.1 Stæður sem eru ferningar með stuðla aðra en 1
9.4.2 Að umrita stæður í öðru veldi
9.4.3 Staðalform og þættir í öðru veldi
9.4.4 Þrjár mismunandi aðferðir til að leysa jöfnu
9.4.5 Stæða sem er ferningur og þættir í öðru veldi
9.4.6 Æfingar
9.4.7 Samantekt kennslustundar
9.5.0 Yfirlit kennslustundar
9.5.1 Rætur ferninga
9.5.2 Lausnir ritaðar sem ferningsrætur
9.5.3 Óræðar lausnir fundnar með því að fylla í ferninginn
9.5.4 Nákvæmar lausnir fundnar
9.5.5 Æfingar
9.5.6 Samantekt kennslustundar
9.6.0 Yfirlit kennslustundar
9.6.1 Mat á stæðum
9.6.2 Besta aðferðin valin til að leysa jöfnu
9.6.3 Jöfnuformúla annars stigs jafna
9.6.4 Jöfnur leystar með jöfnuformúlu annars stigs jafna
9.6.5 Æfingar
9.6.6 Samantekt kennslustundar
9.7.0 Yfirlit kennslustundar
9.7.1 Mat á stæðum með breytum
9.7.2 Algengar reiknivillur við notkun jöfnuformúlu annars stigs jafna
9.7.3 Mismunandi aðferðir til að athuga lausnir annars stigs jafna
9.7.4 Æfingar í að finna reiknivillur
9.7.5 Æfingar
9.7.6 Samantekt kennslustundar
9.8.0 Yfirlit kennslustundar
9.8.1 Útleiðsla á jöfnuformúlu annars stigs jafna, hluti 1
9.8.2 Útleiðsla á jöfnuformúlu annars stigs jafna, hluti 2
9.8.3 Að skilja að jöfnuformúla annars stigs jafna er samsett úr skrefum þess að fylla í ferninginn
9.8.4 Æfingar
9.8.5 Samantekt kennslustundar
9.9.0 Yfirlit kennslustundar
9.9.1 Topppunktur fundinn út frá topppunktsformi
9.9.2 Mismunandi form annars stigs stæðna
9.9.3 Topppunktsform út frá topppunkti og punkti
9.9.4 Endurritun annars stigs stæðna
9.9.5 Æfingar
9.9.6 Samantekt kennslustundar
9.10.0 Yfirlit kennslustundar
9.10.1 Topppunktur og skurðpunktar falls
9.10.2 Liðun úr þáttuðu formi yfir á staðalform
9.10.3 Að breyta úr staðalformi í topppunktsform
9.10.4 Að endurrita stæður á topppunktsformi
9.10.5 Mismunandi form annars stigs stæðna
9.10.6 Topppunktsform og hnit topppunktsins
9.10.7 Æfingar
9.10.8 Samantekt kennslustundar
Yfirlit verkefnis 9
Jöfnur tveggja lína og ferils
Greining á dýfingarstökki
Línulegt fall og annars stigs fall
Hagnaður af fljótsiglingu
Samantekt 9. hluta
Uppbyggileg mistök
Umræður í kennslustofunni
Gróskuhugarfar
Markmiðasetning
Dreifð upprifjun
Margmiðlunarreglan
Reglan um skapandi nám
Röð eininga og úrræði
Uppbygging kennslustunda og úrræði
Tegundir námsmats og úrræði
Atriðisorðaskrá
Algebra 1 (IS)Kafli 77.17.5 Jöfnur grafhliðrana
77.17 Breyting á topppunkti
7.17.5 Jöfnur grafhliðrana
FYRRI KAFLI
7.17.4 Umbreyting grunnfallsins
NÆSTI KAFLI
7.17.6 Æfingar
7.17.5 • Jöfnur grafhliðrana
Lokaverkefni
Hér er graf sem táknar fallið:
$f(x) = x²$
Notaðu grafteikniverkfæri eða aðra tækni. Teiknaðu í sama hnitakerfi graf sem táknar fallið:
$f(x) = (x − 6)² + 10$
Berðu saman svarið þitt:
Grafið hefur sömu lögun og grafið fyrir f(x) = x², en því hefur verið hliðrað 6 einingar til hægri og 10 einingar upp. Topppunktur þess er í (6, 10).
Grafið sem táknar f(x) = x² er hliðrað 2 einingar til vinstri og 10 einingar niður og speglað þannig að það opnast niður, eins og sýnt er.
Hvaða jafna skilgreinir þennan feril?
Lausn
$//www.w3.org/1998/Math/MathML" display="block" alttext="f(x) = −(x + 2)² − 10"> f (x) = - {(x + 2)}^{2} - 10$
$//www.w3.org/1998/Math/MathML" display="block" alttext="f(x) = (x + 2)² − 10"> f (x) = {(x + 2)}^{2} - 10$
$//www.w3.org/1998/Math/MathML" display="block" alttext="f(x) = −(x + 2)² + 10"> f (x) = - {(x + 2)}^{2} + 10$
$//www.w3.org/1998/Math/MathML" display="block" alttext="f(x) = (x + 2)² + 10"> f (x) = {(x + 2)}^{2} + 10 Svar: f (x) = - {(x + 2)}^{2} - 10 FYRRI KAFLI 7.17.4 Umbreyting grunnfallsins NÆSTI KAFLI 7.17.6 Æfingar $RC("B:1","S:1") (self.__next_f=self.__next_f||[]).push([0]) 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Teiknaðu í sama hnitakerfi graf sem táknar fallið:\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"alg-7-17-5-math-002\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"f(x) = (x − 6)² + 10\",\"props\":{\"mathml\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"block\\\" alttext=\\\"f(x) = (x − 6)² + 10\\\"\u003e\u003cmrow\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e−\u003c/mo\u003e\u003cmn\u003e6\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"para-00005\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Berðu saman svarið þitt:\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eBerðu saman svarið þitt:\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"generated-2-children-6\",\"typeKey\":\"Figure\",\"schemaVersion\":\"1.0.0\",\"variant\":\"default\",\"text\":\"$undefined\",\"props\":{\"src\":\"https://m4u5rs6quwqmofe9.public.blob.vercel-storage.com/openstax/algebra-1/is/65c1dd64b7648e12977967f98a128f35306943a2.jpg\",\"resourceId\":\"65c1dd64b7648e12977967f98a128f35306943a2\",\"__legacyMedia\":true,\"alt\":\"A graph of the parent quadratic function is given in blue on the coordinate plane. The graph of a second parabola is given and labeled with a vertex at the point (6, 10).\",\"width\":556,\"height\":564},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"para-00007\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Grafið hefur sömu lögun og grafið fyrir f(x) = x², en því hefur verið hliðrað 6 einingar til hægri og 10 einingar upp. Topppunktur þess er í (6, 10).\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eGrafið hefur sömu lögun og grafið fyrir \u003ci\u003ef(x) = x²\u003c/i\u003e, en því hefur verið hliðrað 6 einingar til hægri og 10 einingar upp. Topppunktur þess er í (6, 10).\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"para-00008\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Grafið sem táknar f(x) = x² er hliðrað 2 einingar til vinstri og 10 einingar niður og speglað þannig að það opnast niður, eins og sýnt er.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eGrafið sem táknar \u003ci\u003ef(x) = x²\u003c/i\u003e er hliðrað 2 einingar til vinstri og 10 einingar niður og speglað þannig að það opnast niður, eins og sýnt er.\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"generated-2-children-9\",\"typeKey\":\"Figure\",\"schemaVersion\":\"1.0.0\",\"variant\":\"default\",\"text\":\"$undefined\",\"props\":{\"src\":\"https://m4u5rs6quwqmofe9.public.blob.vercel-storage.com/openstax/algebra-1/is/f92b9aa8f9d9d15e3e8bc3fda5ab1cec79e365b1.svg\",\"resourceId\":\"f92b9aa8f9d9d15e3e8bc3fda5ab1cec79e365b1\",\"__legacyMedia\":true,\"alt\":\"A coordinate plane displays a graph of the parent quadratic function in blue. Another parabola, graphed in black, was transformed using the parameters in the question. The x-axis extends from negative 6 to positive 6 with a scale of 2 while the y-axis extends from negative 30 to positive 30 with a scale of 10.\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"para-00009\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Hvaða jafna skilgreinir þennan feril?\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eHvaða jafna skilgreinir þennan feril?\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"para-00011\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"a.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003ea.\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"alg-7-17-5-math-003\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"f(x) = −(x + 2)² − 10\",\"props\":{\"mathml\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"block\\\" alttext=\\\"f(x) = −(x + 2)² − 10\\\"\u003e\u003cmrow\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e−\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e−\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"para-00012\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"b.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eb.\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"alg-7-17-5-math-004\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"f(x) = (x + 2)² − 10\",\"props\":{\"mathml\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"block\\\" alttext=\\\"f(x) = (x + 2)² − 10\\\"\u003e\u003cmrow\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e−\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"para-00013\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"c.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003ec.\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"alg-7-17-5-math-005\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"f(x) = −(x + 2)² + 10\",\"props\":{\"mathml\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"block\\\" alttext=\\\"f(x) = −(x + 2)² + 10\\\"\u003e\u003cmrow\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e−\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"para-00014\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"d.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003ed.\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"alg-7-17-5-math-006\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"f(x) = (x + 2)² + 10\",\"props\":{\"mathml\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"block\\\" alttext=\\\"f(x) = (x + 2)² + 10\\\"\u003e\u003cmrow\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"para-00015\",\"typeKey\":\"Paragraph\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"Svar:\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eSvar:\u003c/p\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]},{\"id\":\"alg-7-17-5-math-007\",\"typeKey\":\"EquationBlock\",\"schemaVersion\":\"1.0.0\",\"variant\":\"$undefined\",\"text\":\"f(x) = −(x + 2)² − 10\",\"props\":{\"mathml\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"block\\\" alttext=\\\"f(x) = −(x + 2)² − 10\\\"\u003e\u003cmrow\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e−\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e−\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\"},\"content\":\"$undefined\",\"metadata\":\"$undefined\",\"sourceType\":\"legacy\",\"children\":[]}]}],\"sectionNodeId\":\"f9887688-381a-42da-b2d7-959d4723698a\",\"bookSlug\":\"algebra-1\",\"sectionSlug\":\"7-17-5-equations-of-graph-translations\",\"locale\":\"is\",\"renderModel\":{\"surface\":\"READER\",\"nodes\":[{\"blockId\":\"page_7c09d1c0-e1ca-4ed3-82cd-1866371d49c7_titlecreatedbycookbook\",\"typeKey\":\"Heading\",\"variant\":null,\"orderIndex\":0,\"tokenRefs\":[\"typography.heading\",\"spacing.block\"],\"text\":\"7.17.5 Jöfnur grafhliðrana\",\"props\":{\"level\":2},\"children\":[]},{\"blockId\":\"generated-1\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":1,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"7.17.5 • Jöfnur grafhliðrana\",\"props\":{\"__sourceHtml\":\"\u003cp class=\\\"folio-module\\\"\u003e7.17.5 • Jöfnur grafhliðrana\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"sect-00001\",\"typeKey\":\"Section\",\"variant\":null,\"orderIndex\":2,\"tokenRefs\":[\"spacing.section\"],\"text\":\"Lokaverkefni\",\"props\":{\"title\":\"Lokaverkefni\",\"depth\":\"1\"},\"children\":[{\"blockId\":\"para-00001\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":3,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"Hér er graf sem táknar fallið:\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eHér er graf sem táknar fallið:\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"alg-7-17-5-math-001\",\"typeKey\":\"EquationBlock\",\"variant\":null,\"orderIndex\":4,\"tokenRefs\":[\"math.block\"],\"text\":\"f(x) = x²\",\"props\":{\"mathml\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"block\\\" alttext=\\\"f(x) = x²\\\"\u003e\u003cmrow\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/math\u003e\"},\"children\":[]},{\"blockId\":\"generated-2-children-2\",\"typeKey\":\"Figure\",\"variant\":\"default\",\"orderIndex\":5,\"tokenRefs\":[\"figure.default\",\"typography.caption\"],\"text\":\"A graph of the parent quadratic function is given in blue on the coordinate plane. The x-axis extends from negative 6 to 6 with a scale of 2. The y-axis extends from negative 30 to 30 with a scale of 10.\",\"props\":{\"src\":\"https://m4u5rs6quwqmofe9.public.blob.vercel-storage.com/openstax/algebra-1/is/95133170df377117169b0f4e25c3315ccced783f.svg\",\"resourceId\":\"95133170df377117169b0f4e25c3315ccced783f\",\"__legacyMedia\":true,\"alt\":\"A graph of the parent quadratic function is given in blue on the coordinate plane. The x-axis extends from negative 6 to 6 with a scale of 2. The y-axis extends from negative 30 to 30 with a scale of 10.\"},\"children\":[]},{\"blockId\":\"para-00003\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":6,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"Notaðu grafteikniverkfæri eða aðra tækni. Teiknaðu í sama hnitakerfi graf sem táknar fallið:\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eNotaðu grafteikniverkfæri eða aðra tækni. Teiknaðu í sama hnitakerfi graf sem táknar fallið:\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"alg-7-17-5-math-002\",\"typeKey\":\"EquationBlock\",\"variant\":null,\"orderIndex\":7,\"tokenRefs\":[\"math.block\"],\"text\":\"f(x) = (x − 6)² + 10\",\"props\":{\"mathml\":\"\u003cmath xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"block\\\" alttext=\\\"f(x) = (x − 6)² + 10\\\"\u003e\u003cmrow\u003e\u003cmrow\u003e\u003cmi\u003ef\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmrow\u003e\u003cmo stretchy=\\\"false\\\"\u003e(\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e−\u003c/mo\u003e\u003cmn\u003e6\u003c/mn\u003e\u003cmo stretchy=\\\"false\\\"\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e10\u003c/mn\u003e\u003c/mrow\u003e\u003c/math\u003e\"},\"children\":[]},{\"blockId\":\"para-00005\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":8,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"Berðu saman svarið þitt:\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eBerðu saman svarið þitt:\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"generated-2-children-6\",\"typeKey\":\"Figure\",\"variant\":\"default\",\"orderIndex\":9,\"tokenRefs\":[\"figure.default\",\"typography.caption\"],\"text\":\"A graph of the parent quadratic function is given in blue on the coordinate plane. The graph of a second parabola is given and labeled with a vertex at the point (6, 10).\",\"props\":{\"src\":\"https://m4u5rs6quwqmofe9.public.blob.vercel-storage.com/openstax/algebra-1/is/65c1dd64b7648e12977967f98a128f35306943a2.jpg\",\"resourceId\":\"65c1dd64b7648e12977967f98a128f35306943a2\",\"__legacyMedia\":true,\"alt\":\"A graph of the parent quadratic function is given in blue on the coordinate plane. The graph of a second parabola is given and labeled with a vertex at the point (6, 10).\",\"width\":556,\"height\":564},\"children\":[]},{\"blockId\":\"para-00007\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":10,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"Grafið hefur sömu lögun og grafið fyrir f(x) = x², en því hefur verið hliðrað 6 einingar til hægri og 10 einingar upp. Topppunktur þess er í (6, 10).\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eGrafið hefur sömu lögun og grafið fyrir \u003ci\u003ef(x) = x²\u003c/i\u003e, en því hefur verið hliðrað 6 einingar til hægri og 10 einingar upp. Topppunktur þess er í (6, 10).\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"para-00008\",\"typeKey\":\"Paragraph\",\"variant\":null,\"orderIndex\":11,\"tokenRefs\":[\"typography.body\",\"spacing.block\"],\"text\":\"Grafið sem táknar f(x) = x² er hliðrað 2 einingar til vinstri og 10 einingar niður og speglað þannig að það opnast niður, eins og sýnt er.\",\"props\":{\"__sourceHtml\":\"\u003cp\u003eGrafið sem táknar \u003ci\u003ef(x) = x²\u003c/i\u003e er hliðrað 2 einingar til vinstri og 10 einingar niður og speglað þannig að það opnast niður, eins og sýnt er.\u003c/p\u003e\"},\"children\":[]},{\"blockId\":\"generated-2-children-9\",\"typeKey\":\"Figure\",\"variant\":\"default\",\"orderIndex\":12,\"tokenRefs\":[\"figure.default\",\"typography.caption\"],\"text\":\"A coordinate plane displays a graph of the parent quadratic function in blue. Another parabola, graphed in black, was transformed using the parameters in the question. The x-axis extends from negative 6 to positive 6 with a scale of 2 while the y-axis extends from negative 30 to positive 30 with a scale of 10.\",\"props\":{\"src\":\"https://m4u5rs6quwqmofe9.public.blob.vercel-storage.com/openstax/algebra-1/is/f92b9aa8f9d9d15e3e8bc3fda5ab1cec79e365b1.svg\",\"resourceId\":\"f92b9aa8f9d9d15e3e8bc3fda5ab1cec79e365b1\",\"__legacyMedia\":true,\"alt\":\"A coordinate plane displays a graph of the parent quadratic function in blue. Another parabola, graphed in black, was transformed using the parameters in the question. 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