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QuadraticsUnitTestReview• Part1(Non-Calculator):Wednesday,December20• Part2(Calculator):Thursday,December21• Therewillbecumulativematerialfrompasttestsinamultiple-choiceformat,likethefinalexam

willbeattheendofthesemester.Theseconceptsarenotcoveredinthisreview.Non-CalculatorSection:1. Graphthefollowingquadraticequationsinstandardform.Besuretoidentifyallkeyfeaturesandfill

inthetablewiththeorderedpairsyouareplottingonthegraph.Showallwork!a) 𝑦 = 𝑥! − 2𝑥 + 5

i) AxisofSymmetry:

ii) Vertex:

iii) Y-Intercept:

b) 𝑦 = −2𝑥! − 8𝑥 − 5i) AxisofSymmetry:

ii) Vertex:

iii) Y-Intercept:

iv) Isthevertexamaxofmin?

x

y

x

y

2. Graphthefollowingquadraticequationsinvertexform.Besuretoidentifyallkeyfeaturesandfillinthetablewiththeorderedpairsthatyouareplottingonthegraph.Showallnecessarywork!a) 𝑦 = − 𝑥 − 2 ! + 1

i) Vertex:

ii) AxisofSymmetry:

iii) Y-Intercept:

iv) Isthevertexamaxoramin?

b) 𝑦 = !!(𝑥 − 4)! + 1

i) Vertex:

ii) AxisofSymmetry:

iii) Y-Intercept:

iv) Isthevertexamaxoramin?

v) 3. Computethesum,differenceorproductofthefollowingcomplexnumbers.Useaseparatesheetof

papertoshowyourworktoreceivecredit.

4. Simplifythecomplexradicals.

a) −36 c) −100 e) −81 f) −49

b) −20 d) −28 f) −300 g) −42

x

y

x

y

CalculatorSection:1.Thetablebelowshowsthedatathatrepresentstheheightofaballthrownbyashot-putterasittravelsadistanceofxmeters.

a)Definethevariablesxandy: x= y= b)Findthequadraticmodeltofitthisdata. c)Findtheheightoftheballifittravelsadistanceof55meters.

d)Findthedistancetheballtraveledwhenit’sataheightof20meters.2.Usethegiventabletoanswerthefollowingquestions: a)Definethevariablesxandy: x= y= b)Findthequadraticmodeltofitthisdata. c)Useyourmodeltofindthedepthofthewaterafter24hours. d)Findthetimewhenthewateris4feetdeep.3.Theshapeofanarchcanbemodeledbytheequationℎ 𝑥 = −0.025𝑥! + 2𝑥,whereh(x)representstheheightofthearchinfeetandxrepresentsthedistancefromoneendofthearchtotheother. a)Definethevariables: x= y= b)Whatisthewidthofthearch? c)Whatisthemaximumheightofthearch? d)Whatisthereasonabledomainandrange?

Distance(m)

Height(m)

7 820 1533 2447 2660 2467 21

Timeinhours

Depthofwater

4 111 815 1120 10

4.Theheightofaball,infeet,canberepresentedbythefollowingequationwheretistimeinseconds𝑦 = −16𝑡! + 60𝑡 + 20a)Defineeachvariable.x=y=b)Duringwhattimeistheballintheair?

c)Whatisthemaximumheightoftheball?

d)Whatisthereasonabledomainandrange?

5.Solvethefollowingbyeitherfactoring,takingthesquarerootorthequadraticformula.Useaseparatepieceofpapertodoyourwork.a)6𝑥! + 5𝑥 = 4 b)𝑥! − 6𝑥 − 3 = 0 c)4𝑥! + 72 = 0 d)𝑥! + 6𝑥 + 8 = 0e)(𝑥 + 5)! + 100 = 0 f)3𝑥! + 4𝑥 + 2 = 0 g)𝑥! − 10𝑥 + 25 = 0h)9𝑥! − 6𝑥 − 11 = 06)Solvethesystemofequations.Forparts(c)and(d)doyouworkonaseparatepieceofpaper.

c)𝑦 = 𝑥! + 4𝑥 − 2a) b)𝑦 = 6𝑥 − 3

d) 𝑦 = 𝑥! − 5𝑥 + 7 𝑦 = 2𝑥 + 1

7)Usethefollowingrepresentationsofthreedifferentquadraticfunctionstoanswerparts(a)-(c).

a)Findthevertexofeachrepresentation.b)Iseachvertexamaxoramin?

c)Whichofthefollowinghastheleast(smallest)min?