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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 warm UP 12 I 122 the 7 4 2 5 38 2 If the 712 2 s 5 HE 34ft's its Quadratic linear ExpTt 5 rgy atx 2 Y 5
Transcript of › uploads › 8 › 8 › 7 › 7 › 88774672 › quadratic... · SECONDARY MATH II // MODULE 1...
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
Page 14
warm UP12
I 122the 7 4 2 5
38 2 Ifthe 7122 s 5HE 34ft's its
Quadratic linearExpTt5 rgy atx 2 Y 5
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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Linear Quadratic Quadraticy 2 118 f 5 2 X y X2t2xt
SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.4
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
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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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 – 1.5
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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