HighSchool:Math2TakeHomePacket

Student’sName:______________Teacher’sName:_____________

School:_____________

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TableofContentsforMath2

Day1………………………….….TransformationsReview

Day2………………TheGraphofaQuadraticFunction

Day3…………………………………….ReviewofFactoring

Day4…………………SolvetheQuadraticbyFactoring

Day5………….SolvebyusingtheQuadraticFormula

Day6……...……………SolvebyCompletingtheSquare

Day7……......…CompletetheSquaretowriteinVertexForm

Day8……..…ApplicationswithQuadratics(WordProblems)

Day9……..TransformationsofQuadraticFunctions

Day10…………....SolvingSystemsofEquations(LinearandQuadratic)

StudentreferenceVideos:https://virtualnerd.com/common-core/hsf-geometry/HSG-CO-congruence/A/5/ORscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos.

Day1:GeometricTransformationsName:_______________________________

____ 1.TheverticesofatriangleareP(–7,5),Q(–4,–8),andR(–7,4).Nametheverticesoftheimagereflected

acrossthex-axis.A. C. B. D.

_____2.TheverticesofatriangleareP(8,–7),Q(–7,–5),andR(7,6).Nametheverticesoftheimagereflectedacross

they-axis.A. C. B. D.

_____3. Describeinwordsthetranslationrepresentedbytherule

(x,y)®(x-2,y+1)A. 2unitstotherightand1unitdownB. 1unittotherightand2unitsdownC. 2unitstotheleftand1unitdownD. 2unitstotheleftand1unitup

_____4. If isreflectedinthey-axisfindthecoordinatesofDA’B’C’.

____5.WhichtransformationcorrectlymapsfigureAtofigureBshownbelow?

_____6.G(-9,15)isrotated90degreescounterclockwise.WhatarethecoordinatesofG’? A.(15,-9) C.(-9,-15) B.(15,9) D.(-15,-9)

A. rotationB. dilationC. reflectionD. translation

A. A’(1, –2), B’(1, –4), C’(4, –4) C. A’(2, –1), B’(2, –4), C’(4, –4) B. A’(1, 2), B’(1, 4), C’(4, 4) D. A’(–1, 2), B’(–1, 4), C’(–4, 4)

y

x

A

B

_____7.Whichofthefollowingrulesshowsamappingfora180°clockwiserotation?

A. (x,y)(-x,y) C.(x,y)(y,-x)B. (x,y)(-x,-y) D.(x,y)(-y,x)

_____8.Writearuletodescribethefollowingtransformation?

_____9.Namethelineofreflectionforthefollowingreflection.

_____10.Whichgraphshowsarotation?

A. (x, y) ® (x - 7, y +1) B. (x, y) ® (x + 7, y - 1) C. (x, y) ® (-x, y) D. (x, y) ® (-y, x)

A. x- axis B. y -axis C. x = 1 D. y = 1

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

2 4–2–4 x

2

4

–2

–4

y

A.

B.

C.

D.

11. DescribethetransformationthatoccurredtomovepointAontopointA’.Whatinformationdidyouusetocometothisconclusion?

12. Doesthefollowingpictureshowanexampleofareflection,atranslation,orneither?Explainhow

youcametothisconclusion.13. a)Describethetransformationthatmapsfootballhelmet1ontofootballhelmet2.

b)Describethetransformationthatmapsfootballhelmet2ontofootballhelmet3.c)Describeatransformationthatwouldmapfootballhelmet1directlyontofootballhelmet3.

Studentreferencevideos:https://virtualnerd.com/common-core/hsf-functions/HSF-IF-interpreting-functions/C/7/7a/how-do-you-graph-a-quadratic-functionORscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos.DAY2:THEGRAPHOFAQUADRATICFUNCTION

• TheQuadraticEquationiswrittenas:𝑦 = 𝑎𝑥% + 𝑏𝑥 + 𝑐,thisequationhas

adegreeof2.

§ Wherea,bandcareintegercoefficients(wherea 0)• Thegraphofthisequationiscalledaparabola.• ParabolasarefunctionsbecausetheypasstheVerticalLineTest.

AxisofSymmetry:Thislineofsymmetryiscalledtheaxisofsymmetry.Itisalwaysaverticallinethatgoesthroughtheturningpointofthecurve.ToFindtheAxisofSymmetry(AOS):𝒙 = *𝒃

𝟐𝒂

TurningPoint:Isanothertermforthevertexoftheparabola.The“vertex”hasthecoordinatesof.

ToFindTurningPoint(VERTEX):Findtheaxisofsymmetry,thensubstitutethatvalueinplaceofxintheequation..*/

%0, 𝑓 3*/

%0, 45

Rootsoftheequationarethepointswheretheparabolacrossesthex–axis!HowtoGraphParabolas:

1.Findtheaxisofsymmetrybyusingtheformula.2.Substitutethexvaluebackintothe

equationtofindtheturningpointanddescribeitasamaxorminpt. 3.Makeatableofvalues. 4.Graphthepoints.

¹

( )yx,

When “a” is positive, the parabola opens: UP Where the curve reaches a MINIMUM.

When “a” is negative, the parabola opens: DOWN Where the curve reaches a MAXIMUM.

EX1:GRAPH:

EX2:GRAPH: EXPLORINGTHEGRAPHEDQUADRATICEQUATIONStudent reference videos: https://virtualnerd.com/common-core/hsa-algebra/HSA-REI-equations-inequalities-reasoning/B/4/4b/two-solutions-by-graphingORscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos. Thex–intercepts(whenx=0)oftheparabola arecalledtheSOLUTIONSorROOTSoftheequation( )Howmanyrootsarepossibletoobtainfromaquadraticequation?Drawapicturetoillustrateeachsituation

4xxy 2 -=

32xxy 2 +--=

cbxaxy ++= 2

02 =++ cbxax

x

y

x

y

x

y

EX1.Giventhefollowinggraphoftheequationy=x2–7x+10.Answerthefollowingquestions.

Whatistheaxisofsymmetry?__________Whatarethecoordinatesoftheturningpoint?________

IstheT.P.amaxorminimumpoint?________Howmanyrootsarethere?__________Whatarethesolutionsofthisequation?_____Whatarethesolutionscalled?________

EX2.GRAPH:

Whatistheaxisofsymmetry?__________

Whatarethecoordinatesoftheturningpoint?_______ IstheT.P.amaxorminimumpoint?________ Howmanyrootsarethere?__________ Whatarethesolutionsofthisequation?________ Whatdoyoucallthesesolutions?__________

56xxy 2 ---=

Day2Practice:PartsofaParabola Name:___________________________Thegraphofaquadraticiscalla________________.Usingthefollowinggraphandwordbank,fillintheboxesprovidedbelowandidentifythekeyparts!x-interceptsvertexy-interceptsx-axisy-axis

Identifythekeypartsofthegivenparabolas.

Studentreferencevideo:https://virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3a/ORscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos.Day3:FactoringandSolving

MultipleChoiceSection

1. If6x2y2werefactoredoutof24x2y3–18x3y2thebinomialleftwouldbe?

A4y–3x B4y2–18x C4x2y–3y D4x2y–6x

2. Whichisthegreatestcommonfactorof12x2+9x3–6x4?

A6x

B3x

C6x2

D3x2

3. Whichofthefollowingisequaltox2+4x+3? A(x+1)(x+3) B(x+2)(x+2) C(x+4)(x–1) D(x–4)(x–1)

4. Whicharethefactorsoftheexpression3x2+23x–8? A(3x+1)(x–8) B(3x–8)(x+1) C(3x–1)(x+8) D(3x–1)(x–8)

5. Whatisthefactoredformof6x2–16x+8? A(6x–2)(x–4)

B2(3x+2)(x+2)

C2(3x–2)(x–2)

D3(3x+2)(x–2)

6. Whichisafactorof2x2–11x–40? A2x+5 B2x–5 C2x–8 D2x+8

7. Thesumoftwicex2addedto7xis–3.Whichofthefollowingcouldbethevalueofx? A–3 B3 C2 D–2

8. Whichshows3x2–8x+4completelyfactored? A(3x–2)(x+2) B(3x+4)(x–1) C(x+4)(3x–1) D(3x–2)(x–2)

9. Whatarethesolutionsforthequadraticequation2x2+x=3?

A–1,

B1,

C1,–

D–1,–

10. Bobissolvingthisequationbyfactoring. 3x2+17x+10=0

Whichexpressioncouldbeoneofhiscorrectfactors?Ax+5

Bx–5 C3x–2 D3x–5

11. Iftheareaoftherectangleshownisgivenbytheexpression3x2+7x–6,andthewidthis(x+3),whichofthefollowingcouldrepresentthelength?

A(3x+2)

B(x+2) C(3x–3) D(3x–2)

32323232

A = 3x2 + 7x – 6

?

(x + 3)

12. Thevolumeofthecubeshownisx3–5x2+6xifoneofthedimensionsisx,whichrepresentsthetwomissingdimensions?

A(x+2)(x–3) B(x+2)(x+3) C(x–2)(x–3) D(x–2)(x+3)

ConstructedResponse.13. Factor.6x3+9x2–12xy

14. Factoroutthegreatestcommonfactor.4a4b–6a2b2+12a3b

15. Factoroutthegreatestcommonfactor.5ab2+10ab

16. Whatarethefactorsofx2+x–6?

x

?

?

17. Writeinfactoredform.6y2–y–2

18. Whatarethefactorsofx2+9x+20?

19. Factor.8b2–10b+3

20. Writeinfactoredform.x2–9

21. Factorcompletely.4x2–16.

22. Whatarethefactorsof9x2–30x+25?

23. Whatvaluesofsmaketheequations2+7s+10=0true?

X=_______________

24. Whatarethesolutionsoftheequationx2–x=6?X=_______________

25. Findx.2x2=11x+6X=_______________

UsetheStudentReferencevideosfromDay3.Day4:SOLVINGQUADRATICEQUATIONSbyFactoringQUADRATICEQUATION: STANDARDFORMofaquadraticequation:( )HOWTOSOLVEQUADRATICEQUATIONS:

Step1: WriteequationinStandardForm. Step2: FactorthequadraticequationStep3: Seteach()=to0andsolveforthevariable.Step5: CheckeachoftherootsintheORIGINALquadraticequation.Substituteyoursolution

inplaceofxandcheckthaty=0.EXAMPLES:Solveeachequation.Checktheroots.1. Findtheroots: 2. Solvefory: 3. Findtheroots: 4. Solvefory:

cbxaxy ++= 2

02 =++ cbxax

035r12r 2 =+-

024y11y2 =++

06x5x 2 =--

28y3y2 =-

5. Findtheroots:

6. Findtheroots: SolvebyfactoringSPECIALQUADRATICS:ex. and ex. Solvethefollowingequations.Checkalltheroots:7. 8. 9. 10. 11. 12.

30xx 2 +=

3x7x3x3 2 -=-0bxax 2 =+ 0cax2 =+

04z2 =- 036a2 =- x4x 2 -=

0x8x 2 =+ 012x3 2 =- 45y5 2 =

StudentReferenceVideo:https://virtualnerd.com/algebra-2/quadratics/formula-discriminant/quadratic-formula/solve-by-quadratic-formula ORscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos.Day5:SolveQuadraticsbyusingtheQuadraticFormula

StudentReferenceVideo:https://virtualnerd.com/algebra-2/quadratics/solve-by-completing-square-roots/complete-square/ ORscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos. Day6:SolvingQuadraticsbyCompletingtheSquare

StudentReferenceVideo:https://virtualnerd.com/algebra-2/quadratics/solve-by-completing-square-roots/complete-square/completing-square-standard-to-vertex-leading-coefficient-not-1 OrscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos.Day7:WRITINGQUADRATICSINVERTEXFORM

BYCOMPLETINGTHESQUAREStandardForm:𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 VertexForm:𝒚 = 𝒂(𝒙 − 𝒉)𝟐 + 𝒌,where(𝒉, 𝒌)isthevertexoftheparabola.

StudentReferenceVideo: https://www.loom.com/share/15dd7e465d7243a5a7d2835dd52dec1aOrscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos.DAY8:APPLICATIONSWITHQUADRATICFUNCTIONSUsingagraph!1. Usingthegraphattheright,Itshowstheheighthinfeetofasmallrockettsecondsafteritislaunched.Thepathoftherocketisgivenbytheequation:h=-16t2+128t.Howlongistherocketintheair?_________Whatisthegreatestheighttherocketreaches?____Abouthowhighistherocketafter1second?_______After2seconds, a.abouthowhighistherocket?_________ b.istherocketgoinguporgoingdown?________After6seconds, a.abouthowhighistherocket?_______ b.istherocketgoinguporgoingdown?________ Doyouthinktherocketistravelingfasterfrom0to1secondorfrom3to4seconds?Explainyouranswer.

Usingtheequation,findtheexactvalueoftheheightoftherocketat2seconds.2.Aballisthrownintheair.Thepathoftheballisrepresentedbytheequation

h=-t2+8t.Graphtheequationovertheinterval0£t£8ontheaccompanyinggrid.Whatisthemaximumheightoftheball?_______________Howlongistheballabove7meter?________________

50

1

100

150

200

250

2 3 4 5 6 7 8 time (seconds)

h (height (feet))

time (seconds)

height (meters)

StudentReferenceVideo: https://www.loom.com/share/891bd2e36409425aa7a6d9a9ddbe2d07OrscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos.SolvingAlgebraically

3. Aftertseconds,aballtossedintheairfromthegroundlevelreachesaheightofhfeetgivenbytheequationh=144t–16t2.

a. Whatistheheightoftheballafter3seconds?

b. Whatisthemaximumheighttheballwillreach?

c. Findthenumberofsecondstheballisintheairwhenitreachesaheightof224feet.

d. Afterhowmanysecondswilltheballhitthegroundbeforerebound?

4. Arocketcarryingfireworksislaunchedfromahill80feetabovealake.Therocketwillfallintolakeafterexplodingatitsmaximumheight.Therocket’sheightabovethesurfaceofthelakeisgivenbyh=-16t2+64t+80.

a. Whatistheheightoftherocketafter1.5second?

b. Whatisthemaximumheightreachedbytherocket?

c. Howlongwillittakefortherockettoreach128feet?

d. Afterhowmanysecondswilltherockethitthelake?

5. Arockisthrownfromthetopofatallbuilding.Thedistance,infeet,betweentherockandthegroundtsecondsafteritisthrownisgivenbyd=-16t2–4t+382.Howlongaftertherockisthrownisit370feetfromtheground?

StudentReferenceVideo:https://www.youtube.com/watch?v=hvyH-WJtMpcOrscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos.Day9:TransformationsofQuadraticFunctions

(StudentReference:seefirstproblem!)Day10:SOLVINGQUADACTIC–LINEARSYSTEMSSolveALGEBRAICALLYTwoequationswillbegiventoyouwiththedirectionstosolvethesystemalgebraically

• Oneequationwillbeaquadratic.• Thesecondequationwillbelinear.

Steps:

1. Solveforyinbothequationssotheyareiny=form.

2. Substitutethelinearequationintothe‘ypart’ofthequadraticequation.

3. Set=to0

4. SinceyournewequationisaquadraticyoumustFACTORTOSOLVEFORX.

YoushouldgetTWOsolutions!

5. Findybysubstitutingyour‘x’intooneoftheequationsandsolvefory.

6. Checksolutions

1.Solvethefollowingsystem:

2𝑥 = 𝑥% − 𝑥 + 2 Settheequationsequaltoeachotheroncetheyarebothiny=form.

−2𝑥 − 2𝑥 Set=to0bysubtracting2xfrombothsides.

0 = 𝑥% − 3𝑥 + 2 Now,factor.

0 = (𝑥 − 2)(𝑥 − 1) Seteach()=0andsolveforx.

2.Findthesolutionsof:

3.Solveforthesolutions:

x2y2xxy 2

=+-=

1yx3x4xy 2

=+-+-=

2yx13x7xy 2

=-+-=

StudentReferenceVideo:https://www.loom.com/share/a42989cfca234c13a4d52df8b162cfd8OrscanthisQRcodeonyoursmartphonetoviewthestudentreferencevideos.

SolveGRAPHICALLYExamples:4. Solvethefollowingsystemofequationsgraphicallyandcheck. 5.Solvethefollowingsystemofequationsgraphicallyandcheck.

3x4xy 2 -+-=1yx =+

4x4xy 2 ++=4x2y +-=

6. Thegraphsoftheequations and intersectin: (1) 1point (2) 2points (3) 3points (4) 4points7. Whichisasolutionorthefollowingsystemofequations? (1) (3,–9) (2) (0,0) (3) (5,5) (4) (6,0)8. Whenthegraphsoftheequations and aredrawnonthesamesetofaxes,

atwhichpointdothegraphsintersect?

(1) (4,2) (2) (5,1) (3) (3,3) (4) (2,4)

2xy = 2x =

15x2y -=

x6xy 2 -=

6x5xy 2 +-= 6yx =+