SECONDARY MATH II // MODULE 3

SOLVING QUADRATICS & OTHER EQUATIONS – 3.7

Mathematics Vision Project

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mathematicsvisionproject.org

3.7

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REA DY Topic:SymmetryandDistanceThegivenfunctionsprovidetheconnectionbetweenpossibleareas,A(x),thatcanbecreatedbyarectangleforagivensidelength,x,andasetamountofperimeter.Youcouldthinkofitasthedifferentamountsofareayoucancloseinwithagivenamountoffencingaslongasyoualwayscreatearectangularenclosure.

1.! ! = ! (10 – ! ) 2.! ! = ! (50 – !) Findthefollowing:a.A(3) =b.A(4) =c.A(6) =d.!(!) = 0e.WhenisA(x)atitsmaximum?Explainorshowhowyouknow.

Findthefollowing:a.A 10 =b.A(20) =c.A(30) =d.A(x) = 0e.WhenisA(x)atitsmaximum?Explainorshowhowyouknow.

3.!(!) = !( 75 – !) 4.!(!) = !( 48 – !) Findthefollowing:a.!(20) =b.!(35) =c.!(40) =d.!(!) = 0e.WhenisA(x)atitsmaximum?Explainorshowhowyouknow.

Findthefollowing:a.A(10) =b.A(20) =c.A(28) =d.A(x) = 0e.WhenisA(x)atitsmaximum?Explainorshowhowyouknow.

READY, SET, GO! Name PeriodDate

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SECONDARY MATH II // MODULE 3

SOLVING QUADRATICS & OTHER EQUATIONS – 3.7

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

3.7

Needhelp?Visitwww.rsgsupport.org

SET Topic:SolveQuadraticEquationsEfficientlyForeachofthegivenquadraticequationsfindthesolutionsusinganefficientmethod.Statethemethodyouareusingaswellasthesolutions.Youmustuseatleastthreedifferentmethods.5.!! + 17! + 60 = 0 6.!! + 16! + 39 = 0 7.!! + 7! – 5 = 0

8.3!! + 14! – 5 = 0 9.!! – 12! = −8 10.!! + 6! = 7

Summarizetheprocessforsolvingaquadraticbytheindicatedstrategy.Giveexamplesalongwithwrittenexplanation,alsoindicatewhenitisbesttousethisstrategy.

11.CompletingtheSquare

12.Factoring

13.QuadraticFormula

GO Topic:GraphingQuadraticsandfindingessentialfeaturesofthegraph.Solvingsystemsofequations.Graphthequadraticfunctionandsupplythedesiredinformationaboutthegraph.

14.!(!) = !! + 8! + 13

a.Lineofsymmetry:b.x-intercepts:c.y-intercept:d.vertex:

47

SECONDARY MATH II // MODULE 3

SOLVING QUADRATICS & OTHER EQUATIONS – 3.7

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

3.7

Needhelp?Visitwww.rsgsupport.org

15.!(!) = !! – 4! – 1

a.Lineofsymmetry:b.x-intercepts:c.y-intercept:d.vertex:

Solveeachsystemofequationsusinganalgebraicmethodandcheckyourwork!

16. 17.

3! + 5! = 153! − 2! = 6

! = −7! + 12! = 5! − 36

18. 19.

! = 2! + 12! = 10! − !!

! = 24! − !!! = 8! + 48

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