chapter 8 fair game review - rusd math -...

Copyright © Big Ideas Learning, LLC Big Ideas Math Algebra All rights reserved. Record and Practice Journal

211

Chapter

8 Fair Game Review

Name_________________________________________________________ Date __________

Graph the linear equation.

1. 2y x= − 2. 2 3y x= − +

3. 3 3y x= − − 4. 4y x=

5. 2y x= − + 6. 3 1y x= +

x

y

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Big Ideas Math Algebra Copyright © Big Ideas Learning, LLC Record and Practice Journal All rights reserved. 212

Chapter

8 Fair Game Review (continued)

Name _________________________________________________________ Date _________

Evaluate the expression when x = 2.

7. 22 4x x− + 8. 2 3 3x x− + +

9. 24 2 5x x− − 10. 22 6 7x x− + −

Evaluate the expression when x = −3.

11. 2 3x x− + + 12. 23 5 2x x+ +

13. 24 3 9x x− − + 14. 2 4 15x x− −

15. The height (in feet) of a ball thrown off a balcony can be represented by 216 28 31,t t− + + where t is time in seconds.

a. Find the height of the ball when 2.t =

b. The ball’s velocity (in feet per second) can be modeled by 32 28.y t= − + Graph the linear equation.

t

y


213

8.1 Graphing y ax= 2 For use with Activity 8.1

Name_________________________________________________________ Date __________

Essential Question What are the characteristics of the graph of the quadratic function =y ax2? How does the value of a affect the graph of =y ax2?

Work with a partner.

• Complete the input-output table.

• Plot the points in the table.

• Sketch the graph by connecting the points with a smooth curve.

• What do you notice about the graphs?

a.

b.

1 ACTIVITY: Graphing a Quadratic Function

x y x= 2

3−

2−

1−

0

1

2

3

−2

1

2

3

4

5

6

7

8

9

10

x654321−3 −2 −1−4−5−6

y

x y x= − 2

3−

2−

1−

0

1

2

3

−2

−3

−4

−5

−6

−7

−8

−9

−10

1

2

x654321−3 −2 −1−4−5−6

y


8.1 Graphing y ax= 2 (continued)

Name _________________________________________________________ Date _________

Work with a partner. Graph each function. How does the value of a affect the graph of 2?=y ax

a. 23y x=

b. 25y x= −

2 ACTIVITY: Graphing a Quadratic Function

1

2

3

4

5

6

7

8

9

10

11

x654321−3 −2 −1−4−5−6

y

y = x2

−4

−6

−8

−10

−12

−14

−16

−18

2

4

6

x654321−3 −2 −1−4−5−6

y

y = x2


215

8.1 Graphing y ax= 2 (continued)

Name_________________________________________________________ Date __________

c. 20.2y x= −

d. 2110

y x=

What Is Your Answer? 3. IN YOUR OWN WORDS What are the characteristics of the graph of the

quadratic function 2 ?y ax= How does the value of a affect the graph of 2 ?y ax= Consider 0, 1, and 0 1a a a< > < < in your answer.

−2

−3

−4

−5

−6

1

2

3

4

5

6

x654321−3 −2 −1−4−5−6

y

y = x2

1

2

3

4

5

6

7

8

9

10

11

x654321−3 −2 −1−4−5−6

y

y = x2


8.1 Practice For use after Lesson 8.1

Name _________________________________________________________ Date _________

Graph the function. Compare the graph to the graph of y x= 2 .

1. 23y x= 2. 223

=y x

3. 265

=y x 4. 24y x= −

5. 243

y x= − 6. 237

y x= −

7. The path of a dolphin jumping out of water can be modeled by

20.096 ,y x= − where x and y are measured in feet. Find the distance and maximum height of the jump.

x

y

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x

y

−8

−12

−16

−4

8 12−8−12

y

−44


217

8.2 Focus of a Parabola For use with Activity 8.2

Name_________________________________________________________ Date __________

Essential Question Why do satellite dishes and spotlight reflectors have parabolic shapes?

Work with a partner. Rays are coming straight down. When they hit the parabola, they reflect off at the same angle at which they entered.

• Draw the outgoing part of each ray so that it intersects the y-axis.

• What do you notice about where the reflected rays intersect the y-axis?

• Where is the receiver for the satellite dish? Explain.

1 ACTIVITY: A Property of Satellite Dishes

−1−2 1 2

1

2

3

y = x214

Incomingangle

x

y

Ray Ray Ray


8.2 Focus of a Parabola (continued)

Name _________________________________________________________ Date _________

Work with a partner. Beams of light are coming from the bulb in a spotlight. When the beams hit the parabola, they reflect off at the same angle at which they entered.

• Draw the outgoing part of each beam. What do they have in common? Explain.

2 ACTIVITY: A Property of Spotlights

−1−2 1 2

1

2

3

y = x212

x

y

Beam

Beam

Beam

Incomingangle

Bulb


219

8.2 Focus of a Parabola (continued)

Name_________________________________________________________ Date __________

What Is Your Answer? 3. IN YOUR OWN WORDS Why do satellite dishes and spotlight

reflectors have parabolic shapes?

4. Design and draw a parabolic satellite dish. Label the dimensions of the dish. Label the receiver.



Name _________________________________________________________ Date _________

Graph the function. Identify the focus.

1. 2y x= − 2. 232

=y x

3. 218

=y x 4. 25y x= −

Write an equation of the parabola with a vertex at the origin and the given focus.

5. ( )0, 3 6. ( )0, 0.1−

7. A metal molding company builds a solar furnace to power its factory. The furnace consists of hundreds of mirrors forming a parabolic dish that reflects the energy of the Sun to a focal point. Write an equation for the cross section of the dish when the receiver is 12 feet from the vertex of the parabola.

x

y

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221

8.3 Graphing = +2y ax c For use with Activity 8.3

Name_________________________________________________________ Date __________

Essential Question How does the value of c affect the graph of = +y ax c2 ?

Work with a partner. Sketch the graphs of both functions in the same coordinate plane. How does the value of c affect the graph of 2y ax c= + ?

a. 2y x= and 2 2y x= +

b. 22y x= and 22 2y x= −

1 ACTIVITY: Graphing = +2y ax c

−2

1

2

3

4

5

6

7

8

9

10

x654321−3 −2 −1−4−5−6

y

−2

1

2

3

4

5

6

7

8

9

10

x654321−3 −2 −1−4−5−6

y


8.3 Graphing = +2y ax c (continued)

Name _________________________________________________________ Date _________

c. 2 4y x= − + and 2 9y x= − + d. 212

y x= and 21 82

y x= −

Work with a partner. Graph each function. Find the x-intercepts of the graph. Explain how you found the x-intercepts.

a. 2 4y x= − b. 22 8y x= −

2 ACTIVITY: Finding x-Intercepts of Graphs

−2

1

2

3

4

5

6

7

8

9

10

x654321−3 −2 −1−4−5−6

y

−2

−3

−4

−5

−6

−7

−8

1

2

3

4

x654321−3 −2 −1−4−5−6

y

−2

−3

−4

−5

−6

−7

−8

1

2

3

4

x654321−3 −2 −1−4−5−6

y

−2

−3

−4

−5

−6

−7

−8

1

2

3

4

x654321−3 −2 −1−4−5−6

y


223

8.3 Graphing = +2y ax c (continued)

Name_________________________________________________________ Date __________

c. 2 1y x= − + d. 21 33

y x= −

What Is Your Answer? 3. IN YOUR OWN WORDS How does the value

of c affect the graph of 2 ?y ax c= + Use a graphing calculator to verify your conclusions.

−2

−3

−4

−5

−6

−7

−8

1

2

3

4

x654321−3 −2 −1−4−5−6

y

−2

−3

−4

1

2

3

4

5

6

7

8

x654321−3 −2 −1−4−5−6

y



Name _________________________________________________________ Date _________

Graph the function. Compare the graph to the graph of .y x= 2

1. 2 6= −y x 2. 2 3= +y x

3. 2 8y x= − + 4. 21 43

= −y x

Describe how to translate the graph of y x= −2 3 to the graph of the given function.

5. 2 5= +y x 6. 2 7= −y x

7. A rock is dropped from a height of 25 feet. The function 216 25h x= − + gives the height h of the rock after x seconds. When does it hit the ground?

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8.4 Graphing = + +2y ax bx c For use with Activity 8.4

Name_________________________________________________________ Date __________

Essential Question How can you find the vertex of the graph of = + +y ax bx c2 ?


• Sketch the graphs of 22 8y x x= − and 22 8 6.y x x= − +

22 8y x x= − 22 8 6y x x= − +

• What do you notice about the x-value of the vertex of each graph?

1 ACTIVITY: Comparing Two Graphs

−2

−3

−4

−5

−6

−7

−8

−9

1

2

3

4

5

6

7

8

9

x654321−3 −2 −1−4−5−6

y

−2

−3

−4

−5

−6

−7

−8

−9

1

2

3

4

5

6

7

8

9

x654321−3 −2 −1−4−5−6

y


8.4 Graphing = + +2y ax bx c (continued)

Name _________________________________________________________ Date _________


• Use the graph in Activity 1 to find the x-intercepts of the graph of 22 8 .y x x= − Verify your answer by solving 20 2 8 .x x= −

• Compare the location of the vertex to the location of the x-intercepts.


• Solve 20 ax bx= + by factoring.

• What are the x-intercepts of the graph of 2 ?y ax bx= +

• Complete the table to verify your answer.

2 ACTIVITY: Comparing x-Intercepts with the Vertex

3 ACTIVITY: Finding Intercepts

x y ax bx= +2

0

ba

−


227

6.2 Graphing = + +y ax bx c2 (continued) 8.4

Name ________________________________________________________ Date __________

Work with a partner. Complete the following logical argument.

What Is Your Answer? 5. IN YOUR OWN WORDS How can you find the vertex of the graph of

2y ax bx c= + + ?

6. Without graphing, find the vertex of the graph of 2 4 3.y x x= − + Check your result by graphing.

4 ACTIVITY: Deductive Reasoning

The x-intercepts of the graph of 2y ax bx= + are 0 and .ba

−

The vertex of the graph of 2y ax bx= + occurs when x = _______________.

The vertices of the graphs of 2y ax bx= + and 2y ax bx c= + + have the same x-value.

The vertex of 2y ax bx c= + + occurs when x = _______________.



Name _________________________________________________________ Date _________

Find (a) the axis of symmetry and (b) the vertex of the graph of the function.

1. 26 12 1= − +y x x 2. 24 83

y x x= − −

Graph the function. Describe the domain and range.

3. 22 16 18y x x= − + − 4. 21 4 53

= + +y x x

Tell whether the function has a minimum or a maximum value. Then find the value.

5. 21 6 15

= + −y x x 6. 25 20 9y x x= − − +

7. The entrance of a tunnel can be modeled

by 21 2 218

y x x= − + − , where x and y

are measured in feet. What is the height of the tunnel?

x

y

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x

y

16

8

16 24 32 408−8


229

Practice For use after Extension 8.4

Extension 8.4

Name_________________________________________________________ Date __________

Graph the function. Compare the graph to the graph of =y x 2 . Use a graphing calculator to check your answer.

1. ( )22y x= − 2. ( )24y x= +

3. ( )27y x= + 4. ( )23.5y x= −

5. ( )26 3y x= + + 6. ( )25 1y x= − +

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Extension 8.4 Practice (continued)

Name _________________________________________________________ Date _________

7. ( )22 8y x= + − 8. ( )22 1 4y x= − −

9. ( )23 4 2y x= − − + 10. ( )21 5 63

y x= + −

Describe how the graph of g(x) compares to the graph of f(x).

11. ( ) ( )9g x f x= − 12. ( ) ( )4 5g x f x= +

13. The profit (in millions) of company A can be modeled by ( )28 10A t= − − + and the profit (in millions) of company B

can be modeled by ( )213 9,B t= − − + where t is time in years.

a. How much greater is company A’s maximum profit than company B’s maximum profit?

b. How many years after company A reached its maximum profit did company B reach its maximum profit?

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8.5 Comparing Linear, Exponential, and Quadratic Functions For use with Activity 8.5

Name_________________________________________________________ Date __________

Essential Question How can you compare the growth rates of linear, exponential, and quadratic functions?

Work with a partner. Three cars start traveling at the same time. The distance traveled in t minutes is y miles.

• Complete each table and sketch all three graphs in the same coordinate plane.

1 ACTIVITY: Comparing Speeds

t y t=

0

0.2

0.4

0.6

0.8

1.0

t ty = −2 1

0

0.2

0.4

0.6

0.8

1.0

t y t= 2

0

0.2

0.4

0.6

0.8

1.0

0.2

0

0.4

0.6

0.8

1.0

t0.20 0.4 0.6 0.8

Time (minutes)

Dis

tan

ce (

mile

s)

1.0

y


8.5 Comparing Linear, Exponential, and Quadratic Functions (continued)

Name _________________________________________________________ Date _________

• Compare the speeds of the three cars. Which car has a constant speed? Which car is accelerating the most? Explain your reasoning.

Work with a partner. Analyze the speeds of the three cars over the given time periods. The distance traveled t minutes is y miles. Which car eventually overtakes the others?

a.

2 ACTIVITY: Comparing Speeds

t y t=

1

2

3

4

t ty = −2 1

1

2

3

4

t y t= 2

1

2

3

4


233

8.5 Comparing Linear, Exponential, and Quadratic Functions (continued)

Name_________________________________________________________ Date __________

b.

What Is Your Answer? 3. IN YOUR OWN WORDS How can you compare the growth rates of

linear, exponential, and quadratic functions? Which type of growth eventually leaves the other two in the dust? Explain your reasoning.

t y t=

4

5

6

7

8

9

t ty = −2 1

4

5

6

7

8

9

t y t= 2

4

5

6

7

8

9



Name _________________________________________________________ Date _________

Plot the points. Tell whether the points represent a linear, an exponential, or a quadratic function.

1. ( ) ( ) ( )1 13, , 2, , 1, 1 , 0, 3 , 1, 99 3

⎛ ⎞ ⎛ ⎞− − −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

2. ( ) ( ) ( ) ( ) ( )0, 1 , 1, 2 , 2, 3 , 3, 2 , 4, 1− −

Tell whether the table of values represents a linear, an exponential, or a quadratic function.

3. 4.

Tell whether the data values represent a linear, an exponential, or a quadratic function. Then write an equation for the function using the form y mx b= + ,

xy ab y ax= = 2, or .

5. ( ) ( ) ( ) ( ) ( )3, 12 , 2, 7 , 1, 2 , 0, 3 , 1, 8− − − − −

6. ( ) ( ) ( ) ( ) ( )1, 0.5 , 0, 2 , 1, 8 , 2, 32 , 3, 128−

7. The table shows the shipping cost c (in dollars) by weight w (in pounds) for items from an online store.

a. Does a linear, an exponential, or a quadratic function represent this situation?

b. How much does it cost to ship a 6-pound item?

x

y

O x

y

O

x 5− 4− 3− 2− 1−

y 0 1− 0 3 8

x 2− 1− 0 1 2

y 5− 3.5− 2− 0.5− 1

Weight, w 1 2 3 4

Cost, c 8.5 11 13.5 16


235

Comparing Graphs of Functions For use with Extension 8.5

Extension 8.5

Name_________________________________________________________ Date __________

You have already learned that the average rate of change (or slope) between any two points on a line is the change in y divided by the change in x. You can find the average rate of change between two points of a nonlinear function using the same method.

In Example 4 on page 428 of your textbook, the function ( ) 216 80 5= − + +f t t t gives the height (in feet) of a water balloon t seconds after it is launched.

a. Complete the table for ( ).f t

b. Graph the ordered pairs from part (a). Then draw a smooth curve through the points.

c. For what values is the function increasing?

For what values is the function decreasing?

d. Complete the tables to find the average rate of change for each interval.

1 ACTIVITY: Rates of Change of a Quadratic Function

15

30

45

60

75

90

120

t3 4 5 621

y

105

Time Interval 0 to 0.5 sec 0.5 to 1 sec 1 to 1.5 sec 1.5 to 2 sec 2 to 2.5 sec

Average Rate of Change (ft/sec)

t 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

( )f t

Time Interval 2.5 to 3 sec 3 to 3.5 sec 3.5 to 4 sec 4 to 4.5 sec 4.5 to 5 sec

Average Rate of Change (ft/sec)


Comparing Graphs of Functions (continued) Extension 8.5

Name _________________________________________________________ Date _________

Practice 1. Compared to the average rate of change of a linear function, what do you

notice about the average rate of change in part (d) of Activity 1?

2. Is the average rate of change increasing or decreasing from 0 to 2.5 seconds? How can you use the graph to justify your answer?

3. What do you notice about the average rate of change when the function is increasing and when the function is decreasing?

4. In Example 4 on page 419 of your textbook, the function 2( ) 16 64f t t= − + gives the height of an egg t seconds after it is dropped.

a. Complete the table for ( ).f t

b. Graph the ordered pairs and draw a smooth curve through the points.

c. Describe where the function is increasing and decreasing.

d. Find the average rate of change for each interval in the table. What do you notice?

t 0 0.5 1 1.5 2

( )f t

8

16

24

32

40

48

t1.51.00.5

y56


237

Comparing Graphs of Functions (continued)Extension

8.5

Name_________________________________________________________ Date __________

The graphs show the number y of videos on three video-sharing websites x hours after the websites are launched.

Linear Quadratic Exponential

a. Do the three websites ever have the same number of videos?

b. Complete the table for each function.

Linear

Quadratic

Exponential

2 ACTIVITY: Rates of Change of Different Functions

x

y

12

16

20

8

4

0

32

28

24

4 53210 6

(2, 8)

(4, 16)(3, 12)(1, 4)

(6, 24)(5, 20)

Time (hours)

Nu

mb

er o

f vi

deo

s

Website 1

(0, 0)x

y

60

80

100

40

20

0

160

140

120

4 53210 6

(2, 16)(3, 36)

(0, 0)(1, 4) (4, 64)

Time (hours)

Nu

mb

er o

f vi

deo

s

Website 2

(6, 144)

(5, 100)

x

y

1500

2000

2500

1000

500

0

4000

3500

3000

4 53210 6

Time (hours)

Nu

mb

er o

f vi

deo

s

Website 3

(0, 1)(2, 16)

(3, 64)(4, 256)

(5, 1024)

(6, 4096)

(1, 4)

Time Interval 0 to 1 h 1 to 2 h 2 to 3 h 3 to 4 h 4 to 5 h 5 to 6 h

Average Rate of Change (videos/hour)






Comparing Graphs of Functions (continued) Extension 8.5

Name _________________________________________________________ Date _________

c. What do you notice about the average rate of change of the linear function?

d. What do you notice about the average rate of change of the quadratic function?

e. What do you notice about the average rate of change of the exponential function?

f. Which average rate of change increases more quickly, the quadratic function or the exponential function?

Practice 5. REASONING How does a quantity that is increasing exponentially

compare to a quantity that is increasing linearly or quadratically?

6. REASONING Explain why the average rate of change of a linear function is constant and the average rate of change of a quadratic or exponential function is not constant.

chapter 8 fair game review - rusd math -...

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