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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

  Needhelp?Visitwww.rsgsupport.org

  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:

  𝑥 𝑓(𝑥)

  6 64

  7 128

  8 256

  9 512

  10 1024

  b.

  Typeandcharacteristics?

  Explicitequation:

  Recursiveequation:

  𝑥 𝑓(𝑥)

  6 36

  7 49

  8 64

  9 81

  10 100

  c.

  Typeandcharacteristics?

  Explicitequation:

  Recursiveequation:

  𝑥 𝑓(𝑥)

  6 11

  7 13

  8 15

  9 17

  10 19

  READY, SET, GO! Name PeriodDate

  Answer:6x+21 Answer:-60x+48

  Answer:-15a2+65a Answer:54x2–18x

  Answer:8x2+12x Answer:8a2–20ab Answer:-44x2–8x

  Answer:Ratioof2betweenoutputs,Exponential.

  Answer:Goesbydifferentamounts,newkind.

  Answer:Differenceof2betweenoutputs,Linear.

  Answer:𝒇(𝒙) = 𝟐𝒙 Answer:𝒇(𝒙) = 𝒙𝟐 Answer:𝒇(𝒙) = 𝟐𝒙 − 𝟏

  Answer:𝒇(𝒙) = 𝒇(𝒙 − 𝟏) ∙ 𝟐 𝒇(𝟏) = 𝟐

  Answer:𝒇(𝒙) = 𝒇(𝒙 − 𝟏) + 𝟐𝒙 − 𝟏 𝒇(𝟔) = 𝟑𝟔

  Answer:𝒇(𝒙) = 𝒇(𝒙 − 𝟏) + 𝟐 𝒇(𝟔) = 𝟏𝟏

  Answer:Different,notexpectedstudentscancreateyet.

• 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

  Needhelp?Visitwww.rsgsupport.org

  9.Linear,exponential,oranewkindoffunction?d.

  Typeandcharacteristics?

  Explicitequation:

  Recursiveequation:

  𝑥 𝑓(𝑥)

  -2 -17

  -1 -12

  0 -7

  1 -2

  2 3

  e.

  Typeandcharacteristics?

  Explicitequation:

  Recursiveequation:

  𝑥 𝑓(𝑥)

  -2 1/25

  -1 1/5

  0 1

  1 5

  2 25

  f.

  Typeandcharacteristics?

  Explicitequation:

  Recursiveequation:

  𝑥 𝑓(𝑥)

  -2 9

  -1 6

  0 5

  1 6

  2 9

  10.Graphthefunctionsfromthetablesin#8and#9.Addanyadditionalcharacteristicsyounoticefromthegraph.Placeyouraxessothatyoucanshowall5points.Identifyyourscale.Writeyourexplicitequationabovethegraph.a.Equation:

  b.Equation:

  c.Equation:

  d.Equation:

  e.Equation:

  f.Equation:

  Answer:Differenceof5betweenoutputs,Linear.

  Answer:Ratioof5betweenoutputs,Exponential.

  Answer:Differentamountsbeingadded,newkind.

  Answer:𝒇(𝒙) = 𝟓𝒙 − 𝟕 Answer:𝒇(𝒙) = 𝟓𝒙 Answer:𝒇(𝒙) = 𝒙𝟐 + 𝟓

  Answer:𝒇(𝒙) = 𝒇(𝒙 − 𝟏) + 𝟓 𝒇(𝟏) = −𝟐

  Answer:𝒇(𝒙) = 𝒇(𝒙 − 𝟏) ∙ 𝟓 𝒇(𝟏) = 𝟓

  Answer:𝒇(𝒙) = 𝒇(𝒙 − 𝟏) + 𝟐𝒙 − 𝟏 𝒇(𝟏) = 𝟔

  Answer:Different,notexpectedstudentscancreateyet.

  Answer:𝒇(𝒙) = 𝟐𝒙Answer:𝒇(𝒙) = 𝒙𝟐 Answer:𝒇(𝒙) = 𝟐𝒙 − 𝟏

  Answer:𝒇(𝒙) = 𝟓𝒙 − 𝟕 Answer:𝒇(𝒙) = 𝟓𝒙 Answer:𝒇(𝒙) = 𝒙𝟐 + 𝟓

• 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

  Needhelp?Visitwww.rsgsupport.org

  GO Topic:RatesofChangeIdentifytherateofchangeineachoftherepresentationsbelow.

  11.

  12. 13.

  x f(x)

  25 65

  26 68

  27 71

  28 74

  14.

  f 0 = 7; f n + 1 = f n + 5

  15.

  16.

  Slopeof𝐴𝐵

  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.

  𝑓 −4 = 24 𝑎𝑛𝑑 𝑓 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

  Answer:4Answer:-3

  Answer:3

  Answer:5

  Answer:𝟐𝟓

  Answer:𝟕𝟐= 𝟑.𝟓

  Answer:50lbsperbox

  Answer:.5

  Answer:-6