SECONDARY MATH II // MODULE 1 QUADRATIC FUNCTIONS – 1SECONDARY MATH II // MODULE 1 QUADRATIC...
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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 READY Topic: Multiplying two binomials In the previous RSG, you were asked to use the distributive property on two different terms in the same problem. Example: !"#$%&#' !"# !"#$%"&' 3! 4! + 1 + 2 4! + 1 . You may have noticed that the binomial 4! + 1 occurred twice in the problem. Here is a simpler way to write the same problem: 3! + 2 4! + 1 . You will use the distributive property twice. First multiply 3! 4! + 1 ; then multiply +2 4! + 1 . Add the like terms. Write the x 2 term first, the x-term second, and the constant term last. !" !" + ! + ! !" + ! → !"! ! + !" + !" + ! → !"! ! + !" + !" + ! → !"! ! + !!" + ! Multiply the two binomials. (Your answer should have 3 terms and be in this form !! ! + !" + !.) 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: Distinguishing between linear and quadratic patterns Use first and second differences to identify the pattern in the tables as linear, quadratic, or neither. Write the recursive equation for the patterns that are linear or quadratic. 10. a. Pattern: b. Recursive equation: -3 -23 -2 -17 -1 -11 0 -5 1 1 2 7 3 13 11. a. Pattern: b. Recursive equation: -3 4 -2 0 -1 -2 0 -2 1 0 2 4 3 10 12. a. Pattern: b. Recursive equation: -3 -15 -2 -10 -1 -5 0 0 1 5 2 10 3 15 READY, SET, GO! Name Period Date like terms Simplified form Page 14 I 1.3 set HN I 2 linear f 3 2 y 6X 5 y axatbxtC y 1 21 1 2
Transcript of SECONDARY MATH II // MODULE 1 QUADRATIC FUNCTIONS – 1SECONDARY MATH II // MODULE 1 QUADRATIC...
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
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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I 1.3 set HNI 2
linear
f
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y 6X 5 y axatbxtCy 1 211 2
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
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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
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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
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12. MaryContrarywantstobuildarectangularflowergardensurroundedbyawalkway4meterswide.Theflowergardenwillbe6meterslongerthanitiswide.
a. Therelationshipbetweenthewidthofthegardenandtheperimeterofthewalkway.
b. Therelationshipbetweenthewidthofthegardenandareaofthewalkway.
13. ! = !!!!!
+ 4
14.
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exponential
