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SECONDARY MATH II // MODULE 1

QUADRATIC FUNCTIONS – 1.3

Mathematics Vision Project

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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.

a. Pattern:b. Recursiveequation:

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

12.

a. Pattern:b. Recursiveequation:

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

READY, SET, GO! Name Period Date

liketermsSimplifiedform

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SECONDARY MATH II // MODULE 1

QUADRATIC FUNCTIONS – 1.3

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

1.3

13.

a. Pattern:b. Recursiveequation:

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

14.

a. Pattern:b. Recursiveequation:

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

15.

a. Pattern:b. Recursiveequation:

! !-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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SECONDARY MATH II // MODULE 1

QUADRATIC FUNCTIONS – 1.4

Mathematics Vision Project

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mathematicsvisionproject.org

1.4

GO Topic:Comparinglinearandexponentialratesofchange

Indicatewhichfunctionischangingfaster.

10. 11. 12.

13. 14. 15.

16a.Examinethegraphattheleftfrom0to1.Whi Whichgraphdoyouthinkisgrowingfaster?

b. Now b. Nowlookatthegraphfrom2to3.Whichgraphisgrowingfasterinthisinterval?

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w(x)

m(x)

d(x)

h(x)

g(x)f(x)

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SECONDARY MATH II // MODULE 1

QUADRATIC FUNCTIONS – 1.5

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

1.5 The Tortoise and The Hare

A Solidify Understanding Task

Inthechildren’sstoryofthetortoiseandthehare,theharemocksthetortoiseforbeingslow.Thetortoisereplies,“Slowandsteadywinstherace.”Theharesays,“We’lljustseeaboutthat,”andchallengesthetortoisetoarace.Thedistancefromthestartinglineofthehareisgivenbythefunction:

! = !!(dinmetersandtinseconds)Becausethehareissoconfidentthathecanbeatthetortoise,hegivesthetortoisea1meterheadstart.Thedistancefromthestartinglineofthetortoiseincludingtheheadstartisgivenbythefunction:

! = 2!(dinmetersandtinseconds)

1. Atwhattimedoestheharecatchuptothetortoise?

2. Iftheracecourseisverylong,whowins:thetortoiseorthehare?Why?

3. Atwhattime(s)aretheytied?

4. Iftheracecoursewere15meterslongwhowins,thetortoiseorthehare?Why?

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If It and 4 secondsRabbit

SECONDARY MATH II // MODULE 1

QUADRATIC FUNCTIONS – 1.5

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

1.5

GO Topic:Identifyingdomainandrangefromagraph

Statethedomainandrangeofeachgraph.Useintervalnotationwhereappropriate.

13a.Domain__________b. Range___________

14a.Domain__________b. Range___________

15a.Domain__________b. Range___________

16a.Domain__________b. Range___________

17a.Domain__________b. Range___________

18a.Domain__________b. Range___________

19a.Domain__________b. Range___________

20a.Domain__________b. Range___________

21. Arethedomainsof#19and#20thesame?Explain.

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