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 – 1.5
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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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
1.6 How Does It Grow?
A Practice Understanding Task
Foreachrelationgiven:a. Identifywhetherornottherelationisa
function;b. Determineifthefunctionislinear,exponential,quadraticorneither;c. Describethetypeofgrowthd. Createonemorerepresentationfortherelation.
1. Aplumberchargesabasefeeof$55foraservicecallplus$35perhourforeachhourworkedduringtheservicecall.Therelationshipbetweenthetotalpriceoftheservicecallandthenumberofhoursworked.
2.
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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
3.
4. ! = !! ! − 2 ! + 4
5.
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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
6. ! = !! ! − 2 + 4
7. Therelationshipbetweenthespeedofacarandthedistanceittakestostopwhentravelingatthatspeed.
Speed(mph)
StoppingDistance(ft)
10 12.520 5030 112.540 20050 312.560 45070 612.5
8. Therelationshipbetweenthenumberofdotsinthefigureandthetime,t.
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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
9. Therateatwhichcaffeineiseliminatedfromthebloodstreamofanadultisabout15%perhour.Therelationshipbetweentheamountofcaffeineinthebloodstreamandthenumberofhoursfromthetimetheadultdrinksthecaffeinatedbeverageiftheinitialamountofcaffeineinthebloodstreamis500mg.
10.
.
11. ! = (4! + 3)(! − 6)
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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
12. MaryContrarywantstobuildarectangularflowergardensurroundedbyawalkway4meterswide.Theflowergardenwillbe6meterslongerthanitiswide.
a. Therelationshipbetweenthewidthofthegardenandtheperimeterofthewalkway.
b. Therelationshipbetweenthewidthofthegardenandareaofthewalkway.
13. ! = !!!!!
+ 4
14.
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exponential
