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SECONDARY MATH II // MODULE 1

QUADRATIC FUNCTIONS – 1.1

Mathematics Vision Project

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1.1

READY Topic:DistributivePropertySimplifythefollowingexpressions

1. 3 2x + 7 2. −12 5x − 4

3. 5a −3a + 13 4. 9x 6x − 2

5. !"! 12x + 18 6. !"! 10a − 25b 7. !!"!! 121x + 22

SET Topic:RecognizingLinearExponentialandQuadraticFunctionsIneachsetof3functions,onewillbelinearandonewillbeexponential.Oneofthethreewillbeanewcategoryoffunction.Listthecharacteristicsineachtablethathelpedyoutoidentifythelinearandtheexponentialfunctions.Whataresomecharacteristicsofthenewfunction?Findanexplicitandrecursiveequationforeach.

8. Linear,exponential,oranewkindoffunction?

a.

Typeandcharacteristics?

Explicitequation:

Recursiveequation:

! !(!)6 647 1288 2569 51210 1024

b.


Explicitequation:

Recursiveequation:

! !(!)6 367 498 649 8110 100

c.


Explicitequation:

Recursiveequation:

! !(!)6 117 138 159 1710 19

READY, SET, GO! Name Period Date

Page 2

as

6 121

or

8 2112

1 2 12 I 2It

3,464 372 3140256128 172 t 2 O512256 Stig2 t2 0

2

Exponential ormainton Quadraticegyf fe Linear equal Difrnen

FIX 2 2X Stx X2 Hx 2 1mm mm mm






1.1

9. Linear,exponential,oranewkindoffunction?d.


Explicitequation:

Recursiveequation:

! !(!)-2 -17-1 -120 -71 -22 3

e.


Explicitequation:

Recursiveequation:

! !(!)-2 1/25-1 1/50 11 52 25

f.


Explicitequation:

Recursiveequation:

! !(!)-2 9-1 60 51 62 9

10. Graphthefunctionsfromthetablesin#8and#9.Addanyadditionalcharacteristicsyounoticefromthegraph.Placeyouraxessothatyoucanshowall5points.Identifyyourscale.Writeyourexplicitequationabovethegraph.a. Equation: b. Equation: c. Equation:

d. Equation: e. Equation: f. Equation:

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12 12 I 2

o

fo

55 Dy t 2

Linear exp Quadratic

a






1.1

GO Topic:RatesofChangeIdentifytherateofchangeineachoftherepresentationsbelow.

11. 12. 13.x f(x)25 6526 6827 7128 74

14.f 0 = 7; f n + 1 = f n + 5

15. 16.Slopeof!"A(-3,12)B(-11,-16)

17. Georgeisloadingfreightintoanelevator.Henoticesthattheweightlimitfortheelevatoris1000lbs.Heknowsthatheweighs210lbs.Hehasloaded15boxesintotheelevator.Eachboxweighs50lbs.Identifytherateofchangeforthissituation.

18.Independentvariable 4 5 6 7 8Dependentvariable 5 5.5 6 6.5 7

19.! −4 = 24 !"# ! 6 = −36

4

3

2

1

–1

–2

–3

–4

–6 –4 –2 2 4 6

4

3

2

1

–1

–2

–3

–4

–6 –4 –2 2 4 6

4

3

2

1

–1

–2

–3

–4

–6 –4 –2 2 4 6

Page 4

lope929

2 X

m






1.3

READY Topic:MultiplyingtwobinomialsInthepreviousRSG,youwereaskedtousethedistributivepropertyontwodifferenttermsinthesameproblem.Example:!"#$%&#' !"# !"#$%"&' 3! 4! + 1 + 2 4! + 1 .Youmayhavenoticedthatthebinomial 4! + 1 occurredtwiceintheproblem.Hereisasimplerwaytowritethesameproblem: 3! + 2 4! + 1 .Youwillusethedistributivepropertytwice.Firstmultiply3! 4! + 1 ;thenmultiply+2 4! + 1 .Addtheliketerms.Writethex2termfirst,thex-termsecond,andtheconstanttermlast.!" !" + ! + ! !" + ! → !"!! + !" + !" + ! → !"!! + !" + !" + ! → !"!! + !!" + !

Multiplythetwobinomials.(Youranswershouldhave3termsandbeinthisform!!! + !" + !.)1. ! + 5 ! − 7 2. ! + 8 ! + 3 3. ! − 9 ! − 4

4. ! + 1 ! − 4 5. 3! − 5 ! − 1 6. 5! − 7 3! + 1

7. 4! − 2 8! + 10 8. ! + 6 −2! + 5 9. 8! − 3 2! − 1

SET Topic:DistinguishingbetweenlinearandquadraticpatternsUsefirstandseconddifferencestoidentifythepatterninthetablesaslinear,quadratic,orneither.Writetherecursiveequationforthepatternsthatarelinearorquadratic.

10.

a. Pattern:b. Recursiveequation:

! !-3 -23-2 -17-1 -110 -51 12 73 13

11.


! !-3 4-2 0-1 -20 -21 02 43 10

12.


! !-3 -15-2 -10-1 -50 01 52 103 15


liketermsSimplifiedform

Page 14

1.3 set HW






1.3

13.


! !-3 24-2 22-1 200 181 162 143 12

14.


! !-3 48-2 22-1 60 01 42 183 42

15.


! !-3 4-2 1-1 00 11 42 93 16

16.

a. Drawfigure5.b. Predictthenumberofsquaresinfigure30.Showwhatyoudidtogetyourprediction.

GO Topic:Interpretingrecursiveequationstowriteasequence

Writethefirstfivetermsofthesequence.

17. ! 0 = −5; ! ! = ! ! − 1 + 8 18. ! 0 = 24; ! ! = ! ! − 1 − 5

19. ! 0 = 25; ! ! = 3! ! − 1 20. ! 0 = 6; ! ! = 2! ! − 1

Figure 5Figure 4Figure 3Figure 2Figure 1

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table






1.4

READY Topic:Applyingslopeformula

Calculatetheslopeofthelinebetweenthegivenpoints.Useyouranswertoindicatewhichlineisthesteepest.

1. A(-3,7)B(-5,17) 2. H(12,-37)K(4,-3)

3. P(-11,-24)Q(21,40) 4. R(55,-75)W(-15,-40)

SET Topic:Investigatingperimetersandareas

Adamandhisbrotherareresponsibleforfeedingtheirhorses.Inthespringandsummerthehorsesgrazeinanunfencedpasture.Thebrothershaveerectedaportablefencetocorralthehorsesinagrazingarea.Eachdaythehorseseatallofthegrassinsidethefence.Thentheboysmoveittoanewareawherethegrassislongandgreen.Theporta-fenceconsistsof16separatepiecesoffencingeach10feetlong.Thebrothershavealwaysarrangedthefenceinalongrectanglewithonelengthoffenceoneachendand7piecesoneachsidemakingthegrazingarea700sq.ft.Adamhaslearnedinhismathclassthatarectanglecanhavethesameperimeterbutdifferentareas.Heisbeginningtowonderifhecanmakehisdailyjobeasierbyrearrangingthefencesothatthehorseshaveabiggergrazingarea.Hebeginsbymakingatableofvalues.Helistsallofthepossibleareasofarectanglewithaperimeterof160ft.,whilekeepinginmindthatheisrestrictedbythelengthsofhisfencingunits.Herealizesthatarectanglethatisorientedhorizontallyinthepasturewillcoveradifferentsectionofgrassthanonethatisorientedvertically.Soheisconsideringthetworectanglesasdifferentinhistable.Usethisinformationtoanswerquestions5–9onthenextpage.


Horizontal Vertical

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yzx y 292Xy X y

2 D






1.4

GO Topic:Comparinglinearandexponentialratesofchange

Indicatewhichfunctionischangingfaster.

10. 11. 12.

13. 14. 15.

16a.Examinethegraphattheleftfrom0to1.Whi Whichgraphdoyouthinkisgrowingfaster?

b. Now b. Nowlookatthegraphfrom2to3.Whichgraphisgrowingfasterinthisinterval?

g(x)

f(x)

r(x)

s(x)

q(x)

p(x)

r(x)s(x)

w(x)

m(x)

d(x)

h(x)

g(x)f(x)

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Oum

Sfx dCx mix

O O MxHx

0 Six

olre

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