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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
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.
Typeandcharacteristics?
Explicitequation:
Recursiveequation:
! !(!)6 367 498 649 8110 100
c.
Typeandcharacteristics?
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
SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
1.1
9. Linear,exponential,oranewkindoffunction?d.
Typeandcharacteristics?
Explicitequation:
Recursiveequation:
! !(!)-2 -17-1 -120 -71 -22 3
e.
Typeandcharacteristics?
Explicitequation:
Recursiveequation:
! !(!)-2 1/25-1 1/50 11 52 25
f.
Typeandcharacteristics?
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:
Page 3
12 12 I 2
o
fo
55 Dy t 2
Linear exp Quadratic
a
SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
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
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
1.3 set HW
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
Page 15
table
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
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.
READY, SET, GO! Name Period Date
Horizontal Vertical
Page 19
yzx y 292Xy X y
2 D
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)
Page 21
Oum
Sfx dCx mix
O O MxHx
0 Six
olre