GCSEMATHEMATICSKEYTOPIC

PRACTICESHEETS

DRAWINGQUADRATICGRAPHS

(EDEXCELHIGHER)

ThesequestionsaresuitableforHigherTierstudents.

Allquestionsshouldbedonewithoutacalculator.

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KeyTopicPracticeSheets DrawingQuadraticGraphs(EdexcelHigher)

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1 (a)Completethetableofvaluesfor𝑦 = 𝑥$ + 𝑥 − 1

𝑥 -4 -3 -2 -1 0 1 2

𝑦 11 1 -1 5

(2) (b)Onthegridbelow,drawthegraphof𝑦 = 𝑥$ + 𝑥 − 1forvaluesof𝑥from-4to2

(2)

(TotalforQuestion1is4marks)

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2 (a)Completethetableofvaluesfor𝑦 = 5 − 𝑥$ − 𝑥

𝑥 -4 -3 -2 -1 0 1 2

𝑦 -7 5 5 -1

(2) (b)Onthegridbelow,drawthegraphof𝑦 = 5 − 𝑥$ − 𝑥forvaluesof𝑥from-4to2

(2)

(TotalforQuestion2is4marks)

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3 (a)Completethetableofvaluesfor𝑓(𝑥) = 𝑥$ + 2𝑥 − 7

𝑥 -4 -3 -2 -1 0 1 2

𝑓(𝑥) 1 -8 -4 1

(2) (b)Onthegridbelow,drawthegraphof𝑓(𝑥)fortherange−4 ≤ 𝑥 ≤ 2

(2)

(c)Useyourgraphtoestimatethevalueof𝑓(−2.5)

𝑓 −2.5 =……………………………….(1)

(TotalforQuestion3is5marks)

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4 Davinahasbeengiventhistableofvaluesfor𝑦 = 𝑥$ + 3𝑥 − 4

𝑥 -5 -4 -3 -2 -1 0 1

𝑦 6 0 -4 -6 -6 -4 0

Davina’steacherhasaskedhertodrawthegraphof𝑦 = 𝑥$ + 3𝑥 − 4forvaluesof𝑥from-5to1. Davina’sgraphisshownbelow.

WritedownthreemistakeswithDavina’sgraph.Mistake1………………………………….………………………………….………………………………….………………………………….……………….………………………………….………………………………….………………………………….………………………………….……………….

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Mistake2………………………………….………………………………….………………………………….………………………………….……………….………………………………….………………………………….………………………………….………………………………….……………….Mistake3………………………………….………………………………….………………………………….………………………………….……………….………………………………….………………………………….………………………………….………………………………….……………….

(TotalforQuestion4is3marks)

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5 (a)Completethetableofvaluesfor𝑓(𝑥) = −𝑥$ + 4𝑥 − 3

𝑥 -1 0 1 2 3 4 5

𝑓(𝑥) -8 0 1 -3

(2) (b)Onthegridbelow,drawthegraphof𝑓(𝑥) = −𝑥$ + 4𝑥 − 3forvaluesof𝑥from-1to5

(2)

(c)Useyourgraphtoestimatethevaluesof𝑥when𝑓(𝑥) = −6

𝑥 =…………………………and…………………………(2)

(TotalforQuestion5is6marks)

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6 Mayahasbeengiventhistableofvaluesfor𝑦 = −𝑥$ − 4𝑥 + 3

𝑥 -5 -4 -3 -2 -1 0 1

𝑦 6 0 -4 -6 -6 -4 0

Maya’steacherhasaskedhertodrawthegraphof𝑦 = −𝑥$ − 4𝑥 + 3forvaluesof𝑥from-5to1. Maya’sgraphisshownbelow.

WritedowntwomistakeswithMaya’sgraph.Mistake1………………………………….………………………………….………………………………….………………………………….……………….………………………………….………………………………….………………………………….………………………………….……………….

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Mistake2………………………………….………………………………….………………………………….………………………………….……………….………………………………….………………………………….………………………………….………………………………….……………….

(TotalforQuestion6is2marks)

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7 Thegraphfor𝑦 = 2𝑥$ + 3𝑥 − 5isdrawnbelow.

(a)Statewhethertheturningpointofthisgraphisaminimumoramaximum.

………………..………………………………….(1)

(b)Findtheco-ordinatesofthisturningpoint. Estimateeachofyouranswerstoonedecimalplace.

..…..……...,..…..……...

(2)

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8 (a)Istheturningpointofthegraphfor𝑦 = −𝑥$ + 𝑥aminimumoramaximum? Explainyouranswer. …………………………………………………………………………………………………………….……………..……………………… …………………………………………………………………………………………………………….……………..……………………… …………………………………………………………………………………………………………….……………..……………………… …………………………………………………………………………………………………………….……………..………………………

(2) (b)Whataretheco-ordinatesofthey-interceptforthegraph𝑦 = −𝑥$ + 𝑥? ..…..……...,..…..……...

(1)

(TotalforQuestion8is3marks)

9 Whichofthesearecorrectstatementsaboutthegraph𝑦 = 𝑥$ − 5𝑥 + 1? Tickallcorrectstatements. Theco-ordinatesofthey-interceptare(0,1)

Theturningpointisamaximum Theturningpointisaminimum Thegraphpassesthrough(3,-8)

(TotalforQuestion9is3marks)

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10 Theturningpointofthegraph𝑦 = 𝑥$ − 6𝑥 + 10is(a,b) aandbareintegers. Explain,withtheuseofadiagramorotherwise,whytheturningpointofthegraphcannotlie betweenthecoordinates(5,5)and(7,17).

(TotalforQuestion10is3marks)

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11 Graphsofthefollowingfunctionshavebeendrawnonthegridbelow

Functions

𝑦 = 2𝑥 + 5𝑦 = 𝑥$ + 6𝑥 + 10𝑦 = −𝑥$ − 4𝑥 − 3

𝑦 = 2𝑥

EachgraphhasbeenlabelledGraphA,GraphB,GraphCorGraphD.

Matcheachofthefunctionswithitscorrespondinggraphbycompletingthetablebelow.

Graphs Functions

GraphA

GraphB

GraphC

GraphD

(TotalforQuestion11is3marks)

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12 (a)Completethetableofvaluesfor𝑦 = 𝑥(3 − 𝑥)

𝑥 -2 -1 0 1 2 3 4

𝑦 -10 2 0 -4

(2) (b)Onthegridbelow,drawthegraphof𝑦 = 𝑥(3 − 𝑥)forvaluesof𝑥from-2to4

(2)

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(c)Bydrawingtheline𝑦 = 2𝑥 − 2onthesamegrid,solvetheequations

𝑦 = 3𝑥 − 𝑥$𝑦 = 2𝑥 − 2

𝑥 =………………………,𝑦 =………………………or𝑥 =………………………,𝑦 =………………………

(3)

(TotalforQuestion12is7marks)

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13 (a)Completethetableofvaluesfor𝑦 = 𝑥$ − 3𝑥 − 1

𝑥 -1 0 1 2 3 4 5

𝑦 -1 -1 3 9

(2) (b)Onthegridbelow,drawthegraphof𝑦 = 𝑥$ − 3𝑥 − 1forvaluesof𝑥from-1to5

(2)

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Thesolutionto𝑥$ − 3𝑥 − 1 < 2is𝑎 < 𝑥 < 𝑏 (c)Bydrawingtheline𝑦 = 2onthesamegrid,findestimatesforthevaluesof𝑎and𝑏. Giveyouranswerstoonedecimalplace.

𝑎 =………………………………….

𝑏 =………………………………….(3)

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14 (a)Drawthegraphfor𝑦 = 𝑥$ − 1onthegridbelowforvaluesintherange−3 < 𝑥 < 3

(4)

(b)Onthesamegrid,drawthegraphfor𝑥$ + 𝑦$ = 4

(2)

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(c)Usingyouranswerstoparts(a)and(b),estimatethesolutionstotheequations

𝑥$ + 𝑦$ = 4𝑦 = 𝑥$ − 1

𝑥 =………………………,𝑦 =………………………or𝑥 =………………………,𝑦 =………………………

(3)

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15 (a)Completethetableofvaluesfor𝑦 = 2𝑥$ − 2𝑥 − 4

𝑥 -2 -1 0 1 2 3 4

𝑦 0 -4 8 20

(2) (b)Onthegridbelow,drawthegraphof𝑦 = 2𝑥$ − 2𝑥 − 4forvaluesof𝑥from-2to4

(2)

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Useyourgraphtoanswerthefollowingquestions (c)Estimatethegradientofthecurveatthepoint(3,8)

Gradient=………………………………….(2)

(d)Estimatetheareaenclosedbetweenthecurveandthex-axis. Youmustshowallyourworkingout.

Area=………………………………….(4)

(TotalforQuestion15is10marks)

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