Quadratic Functions - Mathematics Vision Project (MVP) I // MODULE 6 QUADRATIC FUNCTIONS Mathematics...
Transcript of Quadratic Functions - Mathematics Vision Project (MVP) I // MODULE 6 QUADRATIC FUNCTIONS Mathematics...
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The Mathematics Vision Project Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius
© 2017 Mathematics Vision Project Original work © 2013 in partnership with the Utah State Off ice of Education
This work is licensed under the Creative Commons Attribution CC BY 4.0
MODULE 6
Quadratic Functions
ALGEBRA I
A Learning Cycle Approach
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
MODULE 6 - TABLE OF CONTENTS
QUADRATIC FUNCTIONS
6.1 Something to Talk About – A Develop Understanding Task
An introduction to quadratic functions, designed to elicit representations and surface a new type of
pattern and change (F.BF.1, A.SSE.1, A.CED.2)
READY, SET, GO Homework: Quadratic Functions 6.1
6.2 I Rule – A Solidify Understanding Task
Solidification of quadratic functions begins as quadratic patterns are examined in multiple
representations and contrasted with linear relationships (F.BF.1, A.SSE.1, A.CED.2)
READY, SET, GO Homework: Quadratic Functions 6.2
6.3 Scott’s Macho March – A Solidify Understanding Task
Focus specifically on the nature of change between values in a quadratic being linear (F-BF, F-LE)
READY, SET, GO Homework: Quadratic Functions 6.3
6.4 Rabbit Run– A Solidify Understanding Task
Focus on maximum/minimum point as well as domain and range for quadratics (F.BF.1, A.SSE.1,
A.CED.2)
READY, SET, GO Homework: Quadratic Functions 6.4
6.5 The Tortoise and the Hare– A Solidify Understanding Task
Comparing quadratic and exponential functions to clarify and distinguish between each type of growth as
well as how that growth appears in each of their representations (F.BF.1, A.SSE.1, A.CED.2, F.LE.3)
READY, SET, GO Homework: Quadratic Functions 6.5
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
6.6 How Does it Grow – A Practice Understanding Task
Incorporating quadratics with the understandings of linear and exponential functions (F.LE.1, F.LE.2,
F.LE.3)
READY, SET, GO Homework: Quadratic Functions 6.6
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ALGEBRA I // MODULE 1
QUADRATIC FUNCTIONS – 6.1
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
6.1 Something to Talk About
A Develop Understanding Task
Cellphonesoftenindicatethestrengthofthephone’ssignalwithaseriesofbars.Thelogobelowshowshowthismightlookforvariouslevelsofservice.
1. Assumingthepatterncontinues,drawthenextfigureinthesequence.
2. Howmanyblockswillbeinthefigure10?
3. Examinethesequenceoffiguresandfindaruleorformulaforthenumberoftilesinanyfigurenumber.
CCBYSkinnyCasua
lLover
https://flic.kr/p/KVR
sof
1
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.1
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
6.1
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READY Topic:DistributiveProperty
Simplifythefollowingexpressions
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:RecognizingLinearExponentialandQuadraticFunctions
Ineachsetof3functions,onewillbelinearandonewillbeexponential.Oneofthethreewillbeanewcategoryoffunction.Listthecharacteristicsineachtablethathelpedyoutoidentifythelinearandtheexponentialfunctions.Whataresomecharacteristicsofthenewfunction?Findanexplicitandrecursiveequationforeach.
8.Linear,exponential,oranewkindoffunction?
a.
Typeandcharacteristics?
Explicitequation:
Recursiveequation:
! !(!)6 64
7 128
8 256
9 512
10 1024
b.
Typeandcharacteristics?
Explicitequation:
Recursiveequation:
! !(!)6 36
7 49
8 64
9 81
10 100
c.
Typeandcharacteristics?
Explicitequation:
Recursiveequation:
! !(!)6 11
7 13
8 15
9 17
10 19
READY, SET, GO! Name PeriodDate
2
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.1
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
6.1
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9.Linear,exponential,oranewkindoffunction?
d.
Typeandcharacteristics?
Explicitequation:
Recursiveequation:
! !(!)-2 -17
-1 -12
0 -7
1 -2
2 3
e.
Typeandcharacteristics?
Explicitequation:
Recursiveequation:
! !(!)-2 1/25
-1 1/5
0 1
1 5
2 25
f.
Typeandcharacteristics?
Explicitequation:
Recursiveequation:
! !(!)-2 9
-1 6
0 5
1 6
2 9
10.Graphthefunctionsfromthetablesin#8and#9.Addanyadditionalcharacteristicsyounotice
fromthegraph.Placeyouraxessothatyoucanshowall5points.Identifyyourscale.Writeyour
explicitequationabovethegraph.
a.Equation:
b.Equation:
c.Equation:
d.Equation:
e.Equation:
f.Equation:
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.1
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6.1
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GO Topic:RatesofChange
Identifytherateofchangeineachoftherepresentationsbelow.
11.
12. 13.
x f(x)25 65
26 68
27 71
28 74
14.
! 0 = 7; ! ! + 1 = ! ! ) + 5
15.
16.
Slopeof!"A(-3,12)B(-11,-16)
17.Georgeisloadingfreightintoanelevator.Henoticesthattheweightlimitfortheelevatoris1000lbs.He
knowsthatheweighs210lbs.Hehasloaded15boxesintotheelevator.Eachboxweighs50lbs.Identify
therateofchangeforthissituation.
18.
Independentvariable 4 5 6 7 8
Dependentvariable 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
4
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ALGEBRA I // MODULE 1
QUADRATIC FUNCTIONS – 6.2
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
6.2 I Rule!
A Solidify Understanding Task
Marcohasstartedanewblogaboutsportsat
ImaginationHighSchool(mascot:thefightingunicorns)thathehasdecidedtocall“I
Site”.Hecreatedalogoforthewebsitethatlookslikethis:
Heisworkingoncreatingthelogoinvarioussizestobeplacedondifferentpagesonthe
website.Marcodevelopedthefollowingdesigns:
1. Howmanysquareswillbeneededtocreatethesize100logo?
2. Developamathematicalmodelforthenumberofsquaresinthelogoforsizen.
CC
BY
Alic
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ALGEBRA I // MODULE 1
QUADRATIC FUNCTIONS – 6.2
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
Marcodecidestoexperimentwithmakinghislogo“blockier”sothatitlooksstronger.
Here’swhathecameupwith:
3. AssumingthatMarcocontinueswiththepatternasithasbegun,drawthenext
figure,size4,andfindthenumberofblocksinthefigure.
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ALGEBRA I // MODULE 1
QUADRATIC FUNCTIONS – 6.2
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
4. Developamathematicalmodelforthenumberofblocksinalogoofsizen.
5. Comparethemodelsthatyoudevelopedforthefirstsetoflogostothesecondsetoflogos.Inwhatwaysaretheysimilar?Inwhatwaysaretheydifferent?
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.2
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6.2
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READY Topic:DistributivePropertySimplify.Firstusethedistributivepropertyandthencombinetheliketerms.
Example:
!! !! + ! + ! !! + ! → !"!! + !! + !! + ! → !"!! + !! + !! + ! → !"!! + !!! + !
1.2x 5x + 3 + 7 5x + 3
2.8x x + 1 + 2 x + 1
3.6x x − 10 − 1 x − 10
4.1x 3x + 4 + 5 3x + 4
5. 3x 8x + 3 − 4 8x + 3
6.5x 2x + 6 + 2 2! + 6
7.7x −5x + 2 − 13 −5x + 2
8.−4x 12x + 3 + 3 12x + 3
SET Topic:ComparingAreaandperimeterCalculatetheareaandperimeterofeachfigurebelow.Theareamaybewrittenasaproduct.Includethecorrectunitonyouranswer.(Youranswerswillcontainavariable.)9. 10.
a.Perimeter:______________________ a.Perimeter:______________________
b.Area:____________________________ b.Area:____________________________
READY, SET, GO! Name PeriodDate
liketerms
Simplifiedform
(x+1)in
(x+1)inxcm
xcm
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.2
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11. 12.
a.Perimeter:______________________ a.Perimeter:______________________
b.Area:____________________________ b.Area:____________________________
13. 14.
a.Perimeter:______________________ a.Perimeter:______________________
b.Area:____________________________ b.Area:____________________________
15.Comparetheperimetertotheareaineachofproblems(9-14).
Inwhatwayarethenumbersandunitsintheperimetersandareasdifferent?
GO Topic:GreatestCommonFactorFindtheGCFforthegiventerms.
16.15abc2and25a3bc 17.12x5yand32x6y 18.17pqrand51pqr3
19.7x2and21x 20.6x2,18x,and-12 21.4x2and9x
22.11x2y2,33x2y,and3xy2 23.16a2b,24ab,and16b 24.49s2t2and36s2t2
(a+5)ft
(b+3)ft ami
bmi
(x+3)m
(x–2)m
(x+4)in
(x+1)in
9
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.3
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
6.3 Scott’s Macho March
A Solidify Understanding Task
Scott was determined to eat right and get in shape. He
joined a gym and added push-ups to his daily exercise
routine. He started keeping track of the number of push-ups he completed each day in the bar
graph below, with day one showing he completed three push-ups. After four days, Scott was
certain he could continue this pattern of increasing the number of push-ups for at least a few
months.
1. Model the number of push-ups Scott will complete on any given day. Include both explicit and
recursive equations.
CC
BY
Hec
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.3
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
Scott’s gym is sponsoring a “Macho March” promotion. The goal of “Macho March” is to raise money
for charity by doing push-ups. Scott has decided to participate and has sponsors that will donate
money to the charity if he can do a total of at least 500 push-ups, and they will donate an additional
$10 for every 100 push-ups he can do beyond that. So now Scott is going to track the total number
of push-ups done up to any given day of the month.
2. Estimate the total number of push-ups that Scott will do in a month if he continues to increase
the number of push-ups he does each day in the pattern shown above.
3. Draw the diagram that shows the total number of pushups that Scott has done in the month at
the end of each day.
4. How many push-ups will Scott have done after a week?
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.3
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
5. Model the total number of push-ups that Scott has completed on any given day during “Macho
March”. Include both recursive and explicit equations.
6. Will Scott meet his goal and earn the donation for the charity? Will he get a bonus? If so, how much? Explain.
12
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.3
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6.3
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READY Topic:MultiplyingtwobinomialsInthepreviousRSG,youwereaskedtousethedistributivepropertyontwodifferenttermsinthesame
problem.Example:!"#$%&#' !"# !"#$%"&' 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 PeriodDate
liketermsSimplifiedform
13
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.3
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6.3
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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:InterpretingrecursiveequationstowriteasequenceWritethefirstfivetermsofthesequence.
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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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.4
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
6.4 Rabbit Run
A Solidify Understanding Task
Mishahasanewrabbitthatshenamed“Wascal”.ShewantstobuildWascalapensothat
therabbithasspacetomovearoundsafely.Mishahaspurchaseda72footrolloffencingto
buildarectangularpen.
1. IfMishausesthewholerolloffencing,whataresomeofthepossibledimensionsofthepen?
2. IfMishawantsapenwiththelargestpossiblearea,whatdimensionsshouldsheuseforthesides?Justifyyouranswer.
CC
BY
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. Fea
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.4
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
3. Writeamodelfortheareaoftherectangularpenintermsofthelengthofoneside.Includebothanequationandagraph.
4. Whatkindoffunctionisthis?Howdoyouknow?
5.HowdoesthisfunctioncomparetothesecondtypeofblockIlogosinIRule?
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.4
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6.4
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READY Topic:ApplyingslopeformulaCalculatetheslopeofthelinebetweenthegivenpoints.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 PeriodDate
Horizontal Vertical
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.4
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6.4
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5.FillinAdam’stablewithallofthearrangementsforthefence.(Thefirstoneisdoneforyou.)
Lengthin
“fencing”units
Widthin“fencing”
unitsLengthinft. Widthinft. Perimeter(ft)
Area
(ft)2
1unit 7units 10ft 70ft 160ft 700ft2
a. 2units 160ft
b. 3units 160ft
c. 4units 160ft
d. 5units 160ft
e. 6units 160ft
f. 7units 160ft
6.DiscussAdam’sfindings.Explainhowyouwouldrearrangethesectionsoftheporta-fencesothatAdamwillbeabletodolesswork.
7.MakeagraphofAdam’s
investigation.Letlengthbethe
independentvariableand
areabethedependentvariable.
Labelthescale.
8.Whatistheshapeofyourgraph?
9.Explainwhatmakesthisfunction
beaquadratic.
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.4
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6.4
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GO Topic:ComparinglinearandexponentialratesofchangeIndicatewhichfunctionischangingfaster.
10. 11. 12.
13. 14. 15.
16a.Examinethegraphattheleftfrom0to1.
WhiWhichgraphdoyouthinkisgrowingfaster?
b.Nowb.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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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.5
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
6.5 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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BY
Pau
l Dun
leav
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.5
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
5. Usetheproperties! = 2!and! = !!toexplainthespeedsofthetortoiseandthehareinthefollowingtimeintervals:
Interval Tortoise! = !! Hare! = !![0,2)
[2,4)
[4,∞)
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.5
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
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6.5
Needhelp?Visitwww.rsgsupport.org
READY Topic:RecognizingFunctionsIdentifywhichofthefollowingrepresentationsarefunctions.IftherepresentationisNOTafunctionstatehowyouwouldfixitsoitwas.
1.D={(4,-1)(3,-6)(2,-1)(1,2)(0,4)(2,5)} 2.Thenumberofcaloriesyouhaveburnedsincemidnightatanytimeduringtheday.
3.
4.x -12 -8 -6 -4f(x) 25 25 25 25
5.
6.
SET
Topic:Comparingratesofchangeinlinear,quadratic,andexponentialfunctionsThegraphattherightshowsatimevs.distancegraphoftwocarstravelinginthesamedirectionalongthefreeway.7.Whichcarhasthecruisecontrolon?Howdoyouknow?8.Whichcarisaccelerating?Howdoyouknow?9.Identifytheintervalinfigure1wherecarAseemstobegoingfasterthancarB.10.Forwhatintervalinfigure1doescarBseemtobegoingfasterthancarA?11.Whatinthegraphindicatesthespeedofthecars?12.AthirdcarCisnowshowninthegraph(seefigure2).All3carshavethesamedestination.Ifthedestinationisadistanceof12unitsfromtheorigin,whichcardoyoupredictwillarrivefirst?Justifyyouranswer.
READY, SET, GO! Name PeriodDate
12
10
8
6
4
2
5 10
B
A
Figure 1
12
10
8
6
4
2
5 10
CB
A
Figure 2
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.5
Mathematics Vision Project
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6.5
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GO Topic:IdentifyingdomainandrangefromagraphStatethedomainandrangeofeachgraph.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.
8
6
4
2
–2
–4
8
6
4
2
–2
–4
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.6
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
6.6 How Does It Grow?
A Practice Understanding Task
Foreachrelationgiven:
a) Identifywhetherornottherelationisa
function;
b) Determineifthefunctionislinear,exponential,quadraticorneither;
c) Describethetypeofgrowth
d) Createonemorerepresentationfortherelation.
1. Aplumberchargesabasefeeof$55foraservicecallplus$35perhourforeachhour
workedduringtheservicecall.Therelationshipbetweenthetotalpriceoftheservicecalland
thenumberofhoursworked.
2.
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.6
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
3.
4. ! = !! ! − 2 ! + 4
5.
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.6
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements 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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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.6
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
9. Therateatwhichcaffeineiseliminatedfromthebloodstreamofanadultisabout15%
perhour.Therelationshipbetweentheamountofcaffeineinthebloodstreamandthenumber
ofhoursfromthetimetheadultdrinksthecaffeinatedbeverageiftheinitialamountof
caffeineinthebloodstreamis500mg.
10.
.
11. ! = (4! + 3)(! − 6)
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.6
© 2017 Mathematics Vision Project All Rights Reserved for the Additions and Enhancements mathematicsvisionproject.org
12. MaryContrarywantstobuildarectangularflowergardensurroundedbyawalkway4meterswide.Theflowergardenwillbe6meterslongerthanitiswide.a. Therelationshipbetweenthewidthofthegardenandtheperimeterofthegarden.b. Therelationshipbetweenthewidthofthegardenandareaofthewalkway.
13. ! = !!!!!
+ 4
14.
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
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6.6
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READY Topic:Transforminglines1.Graphthefollowinglinearequationsonthegrid.Theequationy=xhasbeengraphedforyou.Foreachnewequationexplainwhatthenumber3doestothegraphofy=x.Payattentiontothe
y-intercept,thex-intercept,andtheslope.Identifywhatchangesinthegraphandwhatstaysthesame.a. y=x+3
b. y=x–3
c. y=3x
2.Thegraphof! = !isgiven.(Seefigure2.)Foreachequationpredictwhatyouthinkthenumber-2willdotothegraph.Thengraphtheequation.
a. ! = ! + (−2)
Prediction:
b. ! = ! – (−2) Prediction:
c. ! = −2! Prediction:
READY, SET, GO! Name PeriodDate
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.6
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
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6.6
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SET
Topic:Distinguishbetweenlinear,exponentialandquadraticfunctionsForeachrelationgiven:
a. Identifywhetherornottherelationisafunction.(Ifit’snotafunction,skipb–d.)b. DetermineifthefunctionisLinear,Exponential,QuadraticorNeither.c. Describethetypeofgrowth.d. Expresstherelationintheindicatedform.
3.Ihad81frecklesonmynosebeforeIbeganusingvanishingcream.AfterthefirstweekIhad27,thenextweek9,then3...a.Function?b.Linear,Exponential,QuadraticorNeitherc.Howdoesitgrow?d.Makeagraph.LabelyouraxesandthescaleShowall4points.
4.
x y0 81
1 80!!
2 80!!
3 80
4 79!!
a.Function?b.Linear,Exponential,QuadraticorNeitherc.Howdoesitgrow?d.Writetheexplicitequation.
5.
a.Function?b.Linear,Exponential,QuadraticorNeitherc.Howdoesitgrow?d.Createatable
6.Speedinmphofabaseballvs.distanceinft.a. Function?b. Linear,Exponential,QuadraticorNeitherc. Howdoesitgrow?d. Predictthedistancethebaseballflies,ifitleavesthebatataspeedof115mph.
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ALGEBRA I // MODULE 6
QUADRATIC FUNCTIONS – 6.6
Mathematics Vision Project
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6.6
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GO Topic:MatchingfunctionrepresentationsMatchthefunctionontheleftwiththeequivalentfunctionontheright.
______7. f x( ) = −2x + 5 a. f x( ) = 5 2( )x ______8.
b.
______9.Iput$7000inasavingsaccountthatpays3%interestcompoundedannually.Iplantoleaveitinthebankfor20years.TheamountIwillhavethen.
c. f (1) = 2; f (n+1) = f (n)+ 2n+ 2
______10.Theareaofthetrianglesbelow.
d.
______11. f 0( ) = 5; f n( ) = 2∗ f n −1( ) e.y+x=0
______12. f 0( ) = 5; f n( ) = f n −1( )− 2
f.! = ! − 1 ! + 3
______13.x -7.75 -¼ ½ 11.6f(x) 7.75 ¼ -½ -11.6
g.A=7000(1.03)20
31