algebra 1 pap name period - colleyville heritage high school

Algebra1PAP Name______________Period____

Unit8NotesandAssignmentsNotesandAssignmentPacket:Youwillbegivenapacketatthebeginningofeachunit.YouwillonlyreceiveONEcopyofthisandyouareresponsibletokeeptrackofit.Ifyoumisplaceit,youmustprintyourownfromGoogleClassroom.UnitAgenda:Youwillalsoreceiveacoloredunitagendaforeachpacket.Thisfirstdayoftheunit,youshouldlookovertheobjectivesandcreateagoalforyourselfthatyouwishtoaccomplish.Aseachobjectiveistaught,youshouldrateyourselfandidentifyagrowthopportunity.Thiscanbedoneinclassorathome.Afterwedotestcorrections,youaretocompletetheunitreflection.Homework/Assignments:Youmuststayontopofyourassignments.Thesewillbechecked(canhappenunannounced)thedayaftertheyareassigned,thedayofthequiz,orthedayofthetest.Youshouldbepreparedeitherway!Itisyourresponsibilitytogiveyourselfandaccuracygradeforeachassignment.Ontestday,youwillbeexpectedtoturninacompletedagenda,packet,andtestreview.AbsentWork:Ifyouareabsent,itisyourresponsibilitytowatchthevideoandcompletethemissingnotes.STAARPractice:Attheendofeachunitpacket,thereisaSTAARpractice.Thesequestionsmustbecompletedbythatunit’sreviewday.

Unit8Outline:SolvingQuadratics8-1Notes:SolvebyFactoring8-1WS:SolvebyFactoring8-2Notes:SolvebySquareRootMethod8-2WS:SolvebySquareRootMethod8-3Notes:SolvebyCompletetheSquare8-3WS:SolvebyCompletetheSquare8-4Notes:SolvebyQuadraticFormula8-4WS:SolvebyQuadraticFormula8-5Notes:SolveusingAllMethods8-5WS:SolveusingAllMethods8-1–8-5Quiz8-6Notes:QuadraticApplications8-6WS:QuadraticApplicationsUnit8STAARReviewUnit8ReviewUnit8Test

2/20/20

1

Factor and Solve

Solve the following.2x – 1= 0

Solve the following.(x + 3) (2x – 1) = 0

Solve the following.(x – 5) (3x + 2) = 0

Solve the following.x (2x + 7) = 0

Factor and Solve.

x2 + 6x + 8 = 0

8-1 Noteshttps://youtu.be/ouxEPWM9iEU

2/20/20

2

Factor and Solve.

2x2 – 5x – 7= 0Factor and Solve

10x2 = –10x

Factor and Solvex2 – 3x = 28

You try!1. 5x2 = 25x 2. x2 – 11x = –18

8-1 Notes

https://youtu.be/ouxEPWM9iEU

Worksheet Solving by Factoring Name _________________________

Solve the quadratics by factoring.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12. –

8-1 WS

13. 14.

15. 16.

17. 18.

19. 20.

21. 22.

23. 24.

25.

8-1 WS

8-2Notes Name________________

SimplifyingRadicals

1. 75 2. 200 3. 48 4. 40 5.3 72 6.-4 243

7.100)* 8.8

)*

SolvebyusingtheSquareRootMethod.

1. x2=81 2.x2=50 3.m2+5=1054.m2-9=31 5.3m2=3 6.2m2+1=19

7.4m2–5=75

https://youtu.be/kDm5dYETrdw

https://youtu.be/fJsPoTJbuBE

SquareRootMethodWS Name______________________

Simplifyeachsquareroot.1. 96 2. 2163. 98 4.3 185. 72 6. 1447.2 45 8. 1759. 343 10. 12

8-2 WS

SquareRootMethodWS Name______________________

Solveeachequationbytakingsquareroots.Makesureyousimplifyyouranswer.11.*+ = 76 12.*+ = 1613.-+ = 21 14..+ = 415.-+ + 8 = 28 16.−61+ = −41417.-+ − 5 = 73 18.72+ + 1 = 2919.21+ + 10 = 210 20.104+ − 10 = 470

8-2 WS

2/21/20

1

SolveusingCompletetheSquare

x2 +2x– 35=0SolveusingCompletetheSquare

x2 - 2x– 15=0

SolveusingCompletetheSquare

x2 +4x=3SolveusingCompletetheSquare

x2 - 8x=-7

SolveusingCompletetheSquare

2x2 - 4x– 14=0SolveusingCompletetheSquare

5x2 +20x+10=-5

Complete the Square

https://youtu.be/fu4qSmlIQFg

8-3 Notes

Complete(the(Square(WS( ( Name____________________________(

Solve(the(equation(by(competing(the(square.((1.(x2(+(2x(–(63(=(0(( ( ( ( ( 2.(m2(–(8m(–(48(=(0((((((((3.(r2(+(2r(–(48(=(–((6((( ( ( ( ( 4.(x2(–(2x(–(8(=(0((((((((5.(n2(+(16n(–(22(=(0( ( ( ( ( 6.(k2(+(2k(–(33(=(0((((((((7.(x2(–(12x(+(26(=(0( ( ( ( ( 8.(b2(+(2b(–(3(=(0((((((((9.(m2(–(2m(–(48(=(0( ( ( ( ( 10.(x2(+(8x(+(12(=(0(((((

8-3 WS

Complete(the(Square(WS( ( Name____________________________(

11.(r2(–(8r(+(21(=(6( ( ( ( ( 12.(x2(+(12x(+(20(=(0((((((((13.(x2(–(2x(=(3( ( ( ( ( ( 14.(k2(+(10k(+(14(=(–(7((((((((15.(7b2(–(14b(–(56(=(0( ( ( ( ( 16.(2x2(+(12x(+(10(=(0((((((((17.(m2(+(18x(=(–(36( ( ( ( ( 18.(r2(+(10r(=(23(((((((((19.(5x2(–(10(=(10v(( ( ( ( ( 20.(4x2(+(16x(=(64((

8-3 WS

2/20/20

1

ìSolve Quadratic EquationsQuadraticFormula

What is a, b, and c?

x2 + 3x −12 = 0

Solve using Quadratic Formula

4x2 +11x − 20 = 0

Solve using Quadratic Formula

x2 − 5x − 24 = 0

Solve using Quadratic Formula

4x2 + 7x −15 = 0

Solve using Quadratic Formula

2x2 + 39 = −18x

8-4 Notes

https://youtu.be/JhGb7LhaQjI

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Kuta Software - Infinite Algebra 1 Name___________________________________

Period____Date________________Using the Quadratic Formula

Solve each equation with the quadratic formula.

1)

m2 − 5

m − 14 = 0 2)

b2 − 4

b + 4 = 0

3)

2

m2 + 2

m − 12 = 0 4)

2

x2 − 3

x − 5 = 0

5)

x2 + 4

x + 3 = 0 6)

2

x2 + 3

x − 20 = 0

7)

4

b2 + 8

b + 7 = 4 8)

2

m2 − 7

m − 13 = −10

-1-

e8-4 WS

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9)

2

x2 − 3

x − 15 = 5 10)

x2 + 2

x − 1 = 2

11)

2

k2 + 9

k = −7 12) 5

r2 = 80

13)

2

x2 − 36 =

x 14)

5

x2 + 9

x = −4

15)

k2 − 31 − 2

k =

−6 − 3

k2 − 2

k 16) 9

n2 =

4 + 7

n

17)

8

n2 + 4

n − 16 = −

n2 18)

8

n2 + 7

n − 15 = −7

-2-

8-4 WS

Solve&Quadratic&Equations&Using&Any&Method& Name_________________________&

Solve&by&Graphing&f(x)&=&x2&–&4&&&&&&&&&&&

Factoring&x2&–&4&=&0&

Square&Root&Method&x2&–&4&=&0&&&&&&&&

Quadratic&Formula&f(x)&=&x2&–&4&&

Complete&the&Square*&x2&–&4&=&0&&&&&&&&&&

Types&of&Solutions&1&Solution:&&&&&2&Solutions:&&&&No&Solution:&&

*Typically,&you&would&not&use&Complete&the&square&when&b&=&0.&This&was&just&to&show&that&all&methods&lead&to&the&same&answers.&

8-5 Notes https://youtu.be/EgVLA35nsck

Name: __________________________________ Date: __________________________

Practice : Quadratics

Solve the quadratic equation using any method. Round your solutions to the nearest hundredth, if necessary. Write which method you chose to use for each problem. 1. 6x² - 216 = 0 2. 8x² = 56 3. 5x² - 10x = 0 4. x² + 8x + 7 = 0 5. x² - 6x + 1 = 0 6. -9x² + 10x = 5 7. -10x² = -50 8. x² - 16x = -64 9. x² + 3x - 8 = 0 10. x² = 14x – 49 11. x² + 6x = 14 12. -5x² + x = 13

8-5 WS

name______________________________________& & & & & date________________________________&

Unit&8:&Notes&Quadratic&Equation&Applications&

Write&an&equation&and&solve&the&following.&&Be&sure&to&identify&your&unknowns.&

1.& If&a&number&is&subtracted&from&its&square&the&result&is&12.&&Find&the&number.&

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2.& Twice&a&number&is&63&less&than&its&square.&&Find&the&number.&

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3.&&& A&negative&number&is&thirty&less&than&its&square.&&Find&the&number.&

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4.&&& The&square&of&a&number&increased&by&17&times&the&number&is&M72.&&Find&the&number.&

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5.& Two&consecutive&negative&even&integers&have&a&product&of&624.&&Find&the&numbers.&

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8-6 Notes. https://youtu.be/lDWZZroeAko

6.&& The&length&of&a&rectangle&is&8&cm&greater&than&twice&its&width.&&Find&the&dimensions&of&the&rectangle&if&its&area&is&42&cm2.&&What&is&the&perimeter?&

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7.& Use&the&formula&h"="rt"–"16t2&where&h&is&height&in&feet,&t&is&time&and&r&is&rate&or&velocity&&to&determine&when&a&potato&will&be&24&feet&high&if&it&is&shot&off&the&ground&from&a&potato&gun&with&an&initial&speed&of&40&ft/sec.&&&

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& How&long&until&the&potato&hits&the&ground?&

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8.&& A&painter&drops&his&paint&brush&from&a&400&foot&building.&&Use&the&vertical&motion&model&(vmm)&to&write&an&equation&that&models&this&situation.&&Use&your&equation&to&find&the&height&of&the&paint&brush&after&4&seconds?&

&(vmm)&h&=&M16t²&+&vt&+&s&&&&h&is&height,&v&is&vertical&force,&s&is&initial&height.&&&

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& When&is&the&paint&brush&still&256&feet&from&the&ground?&

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https://youtu.be/lDWZZroeAko8-6 Notes

Name______________________________________&& & & & & date_________________________&

Unit&8:&Quadratic&Equation&Application&Practice&

Write&an&equation&and&solve&the&following.&&Make&sure&you&identify&your&unknowns.&

1.& If&a&number&is&subtracted&from&its&square&the&result&is&72.&&Find&the&number.&

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2.&&& A&negative&number&is&42&less&than&its&square.&&&Find&the&number.&

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3.&&& Two&consecutive&negative&odd&integers&have&a&product&of&143.&&Find&the&numbers&

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4.&& The&length&of&a&rectangle&is&six&centimeters&less&than&twice&its&width.&&Find&the&dimensions&of&the&rectangle&if&its&area&is&108&cm2.&&&

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5.& The&length&of&a&rectangle&is&eight&centimeters&greater&than&its&width.&&Find&the&dimensions&of&the&rectangle&if&its&area&is&240&cm2.&

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6.& Find&two&consecutive&positive&odd&integers&whose&product&is&195.&

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8-6 WS

7.& One&side&of&a&rectangular&patio&is&5&feet&longer&than&an&adjacent&side.&&If&the&area&of&the&patio&is&104&square&feet,&how&long&is&the&longer&side?&

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8.& A&golf&ball&is&hit&upward&with&an&initial&speed&of&24.5&meters/sec.&&Using&the&formula&h"="rt"–"4.9t2&where&h&is&height&in&meters,&r&is&rate&or&velocity,&and&t&is&time&in&seconds&determine&when&the&ball&is&19.6&meters&high.&

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& When&will&the&ball&hit&the&ground?&

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9.& &A&model&rocket&is&fired&upward&from&the&ground&with&an&initial&velocity&of&160&feet/sec.&&Using&the&formula&h"="rt"–"16t2&where&h&is&height&in&feet,&r&is&rate&or&velocity,&and&t$is&time&in&seconds&determine&when&the&rocket&is&400&feet&high.&

&

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& When&will&the&rocket&hit&the&ground?&

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8-6 WS

Unit8STAARPractice Name________________________

Unit8STAARPractice Name________________________

Unit8Review Name__________________

Simplifythesquareroots.1. 81 2. 75 3. 98 Solvebyusingsquareroots.4.3x2–27=0 5.–7x2=–56 6.9x2–235=206Findtheexactsolutionforeachequationbycompletingthesquare.7.x2–2x–48=08.x2–14x+19=09.3x2+24x=15Solvebyfactoring.10.6x2–2x=0 11.x2+3x=54 12.3x2–4=–x

Unit8Review Name__________________

Solveusingthequadraticformula.13. 14 2 =x 14. 3m2 − 4 = 11m 15. r2 −10r = −22 Solveusinganymethod.16. x2 + 8x +15 = 0 17. x2 = 16 18.2x2–x–36=019.Whataretherootstothefunction? 20.Findthex-interceptsofthefunction. Howmanyrootsdothefollowingequationshave?21. 72 += xy 22. 962 ++= xxy 23. 542 --= xxy

Unit8Review Name__________________

24.Arocketislaunchedfromatopa38-footcliffwithaninitialverticalvelocityof125feetpersecond.Theheightoftherockettsecondsafterlaunchisgivenbytheequationh = −16t 2 +125t + 38 .Howlongaftertherocketislaunchedwillithittheground?Roundyouranswertothenearesttenthofasecond.25.Ifanumberissubtractedfromitssquaretheresultis56.Findthenumber.26.Thelengthofarectangleis5cmlongerthanthewidth.Iftheareaoftherectangleis14squarecm,findthelengthandthewidth.