Name
Date
Class
Chapter Test
CHAPTER
9
Form A
Select the best answer. 1. Which function is quadratic? A 3x ⫺ 2y ⫽ 5 B 5x 2 ⫹ x ⫽ y ⫺ 4
5. Find the axis of symmetry of this parabola. Y
2. The vertex of this parabola shows that the ____ value of the function is ____.
Y
X
X
A maximum, 2 B maximum, 4
A x ⫽ ⫺2 B x ⫽ ⫺1
C minimum, 2 D minimum, 4
6. If you graph y ⫽ x 2 ⫺ 6x ⫹ 9, the . y-intercept would be A ⫺3 B 9
3. Which table of values would you use to 2 graph y ⫽ 3x ? A x ⫺2 ⫺1 0 1 2 B
y
12
3
0
3
12
x
⫺2
⫺1
0
1
2
y
36
9
0
9
36
C x⫽1 D x⫽3
7. The height of a ball in feet is modeled by 2 f x ⫽ ⫺16x ⫹ 96x, where x is the time in seconds after it is hit. How long is the ball in the air? Y
4. Find the zeros of y ⫽ x 2 ⫺ 8x ⫹ 12 from its graph below.
Y
X
A ⫺2 and ⫺6 B 0 and 4 Copyright © by Holt, Rinehart and Winston. All rights reserved.
A 3s B 6s
C 2 and 6 D 4 and ⫺4
167
X
C 12 s D 24 s Holt Algebra 1
Name
Date
CHAPTER
Chapter Test
9
Form A continued
8. Compare the graph of g x x 2 6 2 with the graph of f x x . A g x is wider. B g x is narrower. C g x is translated 6 units down. D g x is translated 6 units up.
11. A toy rocket is launched from a platform that is 10 meters high. The rocket’s height above the ground is modeled by 2 h 5t 5t 10, where h is height in meters and t is time in seconds. Find the time it takes the rocket to reach the ground. A 1s B 2s
9. Use this graph of the quadratic function 2 y x 4x 4 to solve the equation 2 x 4x 4 0.
2 12. Solve x 9 using square roots. A x 3 B x 81
Y
13. Which number completes the square to form a perfect square trinomial?
x 2 12x
A 6 B 24
X
A B C D
x x x x
2 3 or x 1 4 or x 0 5 or x 1
15. Solve 2x 2 9x 4 0 using the Quadratic Formula. A x 4 or x
2 10. Solve x 7x 8 0 by factoring. A x 1 or x 8 B x 1 or x 8
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 168
C 36 D 144
2 14. Solve x 10x 39 by completing the square. A x 13 or x 3 B x 10 164 or x 10 164 C x 5 39 or x 5 39 D x 5 14 or x 5 14
Class
1 __ 2
9 113 B x ___________ 4 16. Find the number of real solutions of the 2 equation x 11x 10 0 using the discriminant. A 0 C 2 B 1 D 3
168
Holt Algebra 1
12/28/05 3:20:45 PM Process Black
Name CHAPTER
9
Date
Class
Chapter Test Form B
Select the best answer. 1. Which function is quadratic? A x 2 4 1
B
4. Find the zero(s) of y x 2 4x 4 from its graph below.
5
Y
y
18
3
6
27
x
3
2
1
0
y
1
1
3
5
C
x
2
0
2
4
y
13
5
3
59
X
D
x
1
5
9
13
y
2
2
0
4
F 2 G 4
2. The vertex of this parabola shows that the value of the function is .
5. Find the axis of symmetry of the graph 2 of y x 10x 16. A x 10 C x 5 B x 8 D x 13
Y
6. If you graph y 2x 2 8x 10, the . y-intercept would be F 18 H 2 G 10 J 5
X
7. The height of a ball in feet is modeled 2 by f x 16x 128x, where x is the time in seconds after it is hit. How long is the ball in the air?
F maximum, 1 G maximum, 4
H minimum, 1 J minimum, 4
Y
3. Which table of values would you use to 2 graph y x 3? A x 2 1 0 1 2
B
C
D
H 2 and 4 J no zeros
y
32
1
0
1
32
x
2
1
0
1
2
y
1
4
9
16
25
x
2
1
0
1
2
y
7
4
3
4
7
x
2
1
0
1
2
y
12
3
0
3
12
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 169
A 4s B 8s
169
X
C 128 s D 256 s Holt Algebra 1
12/28/05 3:20:45 PM Process Black
Name CHAPTER
9
Date
Class
Chapter Test Form B
continued
8. Compare the graph of g x 6x 2 with 2 the graph of f x x . F g x is narrower. G g x is translated up. H g x is translated down. J g x is wider.
12. Solve 9x 2 4 0 using square roots. 9 4 F x __ H x __ 4 9
13. Which number completes the square to form a perfect square trinomial?
9. Use this graph of the quadratic function 2 y 2x 4x 6 to solve the equation 2 2x 4x 6 0.
x 2 7x
49 B ___ D 49 4 2 14. Solve x 8x 18 0 by completing the square. F x 2 or x 6 G x 4 2 or x 4 2 H x 4 34 or x 4 34 J no real solutions
49 C ___ 2
7 A __ 2
Y
3 J x __ 2
2 G x __ 3
X
2 15. Solve 3x 5x 8 using the Quadratic Formula. A x 3 or x 8
8 B x 1 or x __ 3
A x 2 or x 4 B x 1 or x 3
71 ________ C x5 6 D no real solutions
C x 0 or x 2 D x1
16. Find the number of real solutions of the 2 equation x 10x 35 0 using the discriminant. F 0 H 2 G 1 J 3
10. Solve x 12 4x by factoring. F x 2 or x 6 H x 2 or x 6 G x 3 or x 4 J x 3 or x 4 2
11. A stunt diver jumps from the top of a 40-meter platform. The diver’s height 2 above the water is modeled by h 5t 10t 40, where h is height in meters and t is time in seconds. Find the time it takes the diver to reach the water. A 2s C 8s B 4s D 10 s
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 170
170
Holt Algebra 1
12/28/05 3:20:47 PM Process Black
Name
Date
CHAPTER
9
Class
Chapter Test Form C 2 4. Find the zero(s) of y x 5 from its graph below.
Select the best answer. 1. Which function is quadratic? A { 5, 3 , 2, 0 , 1, 3 , 4, 6 } B { 2, 12 , 0, 2 , 2, 8 , 4, 18 } C { 0, 126 , 4, 14 , 8, 2 , 12, 18 } D { 0, 10 , 1, 7 , 2, 2 , 3, 17 }
Y
2. The vertex of this parabola shows that value of the function is . the
Y
X
F 0 G 5
5. Find the axis of symmetry and vertex of 2 the graph of y 2x 12x 5. A x 3, 3, 59 C x 3, 3, 13 B x 3, 3, 23 D x 3, 3, 47
X
F maximum, 3 G maximum, 0
H 0 and 5 J no zeros
2 6. If you graph 3x 18x 6 3y, the . y-intercept would be F 6 H 2 G 3 J 3
H minimum, 3 J minimum, 0
3. Which table of values would you use to 2 graph y 2x 4? A x
2
1
0
1
2
y
72
50
32
18
8
7. The height of a ball in feet is modeled by 2 f x 16x 72x, where x is the time in seconds after it is hit. How long is the ball in the air? Y
B x
2
1
0
1
2
y
12
6
4
6
12
C x
2
1
0
1
2
y
0
6
8
6
0
D
x
2
1
0
1
2
y
12
0
4
0
12
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 171
A 2.25 s B 4.5 s
171
X
C 9s D 81 s Holt Algebra 1
12/28/05 3:20:47 PM Process Black
Name CHAPTER
9
Date
Class
Chapter Test Form C
continued
8. Compared to the graph of f x x 2, the 2 graph of g x 2x 5 is _____. F narrower and translated down G narrower and translated up H wider and translated down J wider and translated up
2 12. Solve 36x 9 16 using square roots. 1 25 F x __ H x ___ 2 36
2 5 G x __ J x __ 3 6 13. Which number completes the square to form a perfect square trinomial?
9. Use this graph of the quadratic function 2 y x 6x to solve the equation 2 x 6x 0.
9x x 2 9 A __ 2
Y
81 1 B __ D ___ 4 4 14. Solve 3x 2 x 2 0.
2 F x 1 or x __ 3
73 ________ G x1 6
7 _______ H x1 3 J no real solutions
X
15. Solve 4x 2 5x 9 using the Quadratic Formula.
A x 6 or x 0 C x 4 or x 2 B x 5 or x 1 D x 1
1 A x 1 or x __ 4 9 B x 1 or x __ 4
2 10. Solve 4x 14x 8 by factoring. F x 2 or x 1
119 __________ C x 5 8 D no real solutions
1 or x 4 G x __ 2
1 or x 8 H x __ 4
16. Find the number of real solutions of the 2 equation 64x 9 48x using the discriminant. F 0 H 2 G 1 J 3
7 J x 0 or x __
4 11. A 2-meter tall soccer player bunts the ball with his head. The ball’s height above the ground is modeled by 2 h 5t 3t 2, where h is height in meters and t is time in seconds. Find the time it takes the ball to reach the ground. 1s C 1s A __ 5 2s B __ 5 Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 172
C 3
D 2s
172
Holt Algebra 1
6/2/06 2:21:57 PM
Name
Date
Class
Chapter Test
CHAPTER
9
Form A 4. Find the zeros of y x 2 x 6 from its graph below.
1. Tell whether this function is quadratic. Explain. 2x y 3x 9
Y
X
2. Identify the vertex of this parabola. Then give the minimum or maximum value of the function.
Y
5. The zeros of the graph of a quadratic function are 2 and 6. What is its axis of symmetry?
X
6. If you graph y x 2 8x 10, what would be the y-intercept?
vertex:
3. Use a table of values to graph 2 y 2x . x
2
1
0
1
7. The height of a ball in meters is modeled 2 by f x 5x 40x, where x is the time in seconds after it is hit. How long is the ball in the air?
2
y
Y
y
4
2
6
4
2
0
2
4
6
x
2
4
6
8
X
10
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 173
173
Holt Algebra 1
6/2/06 2:21:58 PM
Name
Date
CHAPTER
Chapter Test
9
Form A continued
8. Compare the graph of g x x 2 5 2 with the graph of f x x .
Class
11. A stunt diver jumps from the top of a 96-foot platform. The diver’s height above the water is modeled by 2 h 16t 16t 96, where h is height in feet and t is time in seconds. Find the time it takes the diver to reach the water.
9. Use this graph of the quadratic function 2 y x 4 to solve the equation 2 x 4 0.
12. Solve x 2 121 using square roots.
Y
13. Complete the square to form a perfect square trinomial.
x 2 2x
X
14. Solve x 2 4x 32 by completing the square.
15. Solve 3x 2 5x 1 0 using the Quadratic Formula.
16. Find the number of real solutions of the 2 equation x 2x 8 0 using the discriminant.
2 10. Solve x 2x 24 0 by factoring.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 174
174
Holt Algebra 1
12/28/05 3:20:50 PM Process Black
Name
Date
CHAPTER
9
Class
Chapter Test Form B 4. Find the zeros of y ⫽ x 2 ⫺ x ⫺ 6 from its graph below.
1. Tell whether this function is quadratic. Explain. x
⫺2
0
2
4
y
5
⫺1
⫺3
⫺1
Y
Yes
the second differences are constant.
X
2. Identify the vertex of this parabola. Then give the minimum or maximum value of the function.
Y
X
2; 3
5. Find the axis of symmetry of the graph 2 of y ⫽ x ⫺ 12x ⫹ 8.
x6
6. If you graph y ⫽ 5x 2 ⫹ 7x ⫺ 15, what would be the y-intercept?
3, 5
vertex:
15
Minimum is 5.
7. The height of a ball in meters is modeled 2 by f x ⫽ ⫺5x ⫹ 50x, where x is the time in seconds after it is hit. How long is the ball in the air?
3. Use a table of values to graph 2 y ⫽ x ⫺ 4. x
⫺2
y
0
⫺1
0
1
2
3 4 3
Y
0
Y
X
a107c09_Assess.indd 175
X
10 seconds
Copyright © by Holt, Rinehart and Winston. All rights reserved.
175
Holt Algebra 1
5/9/06 1:59:44 PM Process Black
Name
Date
CHAPTER
9
Class
Chapter Test Form B
continued
1 x 2 with 8. Compare the graph of g x __ 3 2 the graph of f x x .
12. Solve 16x 2 1 0 using square roots.
g x has the same axis of symmetry, has the same vertex, and also
1 x __ 4
opens upward, but it is wider. 9. Use this graph of the quadratic function 2 y x 4x 5 to solve the equation 2 x 4x 5 0.
13. Complete the square to form a perfect square trinomial.
25 ___
Y
4
x 5x 2
14. Solve x 2 6x 13 0 by completing the square.
X
x 3 22 or x 3 22
15. Solve 2x 2 7x 8 using the Quadratic Formula.
x 5 or x 1 10. Solve x 2 18 11x by factoring.
no real solutions
x 2 or x 9 11. A toy rocket is launched from a platform that is 48 feet high. The rocket’s height above the ground is modeled by 2 h 16t 32t 48, where h is height in feet and t is time in seconds. Find the time it takes the rocket to reach the ground.
16. Find the number of real solutions of the 2 equation x 18x 81 0 using the discriminant.
1 one real solutions 3 seconds
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 176
176
Holt Algebra 1
12/28/05 3:20:52 PM Process Black
Name
Date
CHAPTER
9
Class
Chapter Test Form C 2 4. Find the zeros of y x 4x 5 from its graph below.
1. Tell whether this function is quadratic. Explain.
{ 7, 256 , 5, 16 , 3, 0 , 1, 16 }
Y
2. Identify the vertex of this parabola. Then give the minimum or maximum value of the function.
Y
X
5. Find the axis of symmetry and vertex of 2 the graph of y 2x 20x 40.
X
axis of symmetry:
vertex: 6. If you graph 2y 8 6x 2 10x, what will be the y-intercept?
vertex:
3. Use a table of values to graph 2 y 3x 8. x
2
1
0
1
7. The height of a ball in meters is modeled 2 by f x 5x 36x, where x is the time in seconds after it is hit. How long is the ball in the air?
2
y Y
Y
X
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 177
177
X
Holt Algebra 1
12/28/05 3:20:53 PM Process Black
Name CHAPTER
9
Date
Class
Chapter Test Form C
continued
8. Compare the graph of g x x 2 3 2 with the graph of f x x .
12. Solve 4x 2 11 36 using square roots.
13. Complete the square to form a perfect square trinomial. 9. Use this graph of the quadratic function 2 y x 2x to solve the equation 2 x 2x 0.
3x x 2 __ 5
Y
14. Solve 2x 2 x 8 0 by completing the square.
X
15. Solve 3x 1 5x 2 using the Quadratic Formula.
16. Find the number of real solutions of the 2 equation 4x 6 7x using the discriminant.
10. Solve 26x 15 8x by factoring. 2
11. A 6-foot tall soccer player bunts the ball with his head. The ball’s height above the ground is modeled by 2 h 16t 10t 6, where h is height in feet and t is time in seconds. Find the time it takes the ball to reach the ground.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c09_Assess.indd 178
178
Holt Algebra 1
12/28/05 3:20:54 PM Process Black
Answer Key
continued
Chapter Test Form A
Chapter Test Form C
1. B
1. D
2. C
2. J
3. A
3. B
4. C
4. J
5. B
5. C 6. H
6. B
7. B
7. B
8. F
8. D 9. A 10. A 11. B 12. A
9. A 10. G 11. B 12. J 13. D
13. C
14. F
14. A
15. D
15. A
16. G
16. C Chapter Test Form B
Chapter Test Form A
1. A
1. No the the function cannot be written in 2 the form y ax bx c.
2. G
2. 1, 3 maximum is 3.
3. C
3.
4. F 5. C
x
2
1
0
1
2
y
8
2
0
2
8
Y
6. G
7. B 8. F
9. B
10. H
X
11. B 12. G
13. B
14. J 15. B
16. F
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107_Assess_Answer.indd 283
283
Holt Algebra 1
6/2/06 2:13:09 PM
Answer Key
continued
4. 2 and 3
3.
5. x 4
x
2
1
0
1
2
y
0
3
4
3
0
6. 10
Y
7. 8 seconds
Y
X
4. 2; 3
X
5. x 6
8. g x has the same width, same axis of symmetry, and also opens upward, but its vertex is translated 5 units down to 0, 5 .
6. 15 7. 10 seconds Y
9. x 2 or x 2
10. x 4 or x 6
11. 3 seconds
12. x 11
13. 1
14. x 4 or x 8 5 13 15. x _________
6
16. 0 (no real solutions)
X
8. g x has the same axis of symmetry, has the same vertex, and also opens upward, but it is wider.
Chapter Test Form B 1. Yes, the second differences are constant. 2. 3, 5 Minimum is 5.
9. x 5 or x 1 10. x 2 or x 9 11. 3 seconds 1 12. x __ 4 25 13. ___ 4 14. x 3 22 or x 3 22
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107_Assess_Answer.indd 284
284
Holt Algebra 1
6/2/06 2:13:10 PM
Answer Key
continued
x
2
1
0
1
2
3 or x __ 5 10. x __ 4 2 3 second 11. __ 8 5 12. x __ 2 9 13. ____ 100 14. no real solutions 29 ________ 15. x 3 10 16. 2 two real solutions
y
4
5
8
5
4
Performance Assessment
15. no real solutions 16. 1 one real solutions Chapter Test Form C 1. No the second differences are not constant. 2. 0, 4 maximum is 4. 3.
1. 20, 24, 40, or 50 ft
Y
2. 10 w, 12 w, 20 w, or 25 w
2 2 3. A w 10w, A w 12w, A 2 2 w 20w, or A w 25w
5. 0 and 10, 0 and 12, 0 and 20, or 0 and 2 25; the widths that create an area of 0 ft .
X
6. x 5, x 6, x 10, or x 12.5; the x-value is one-fourth the amount of chain link.
7. (5, 25), (6, 36), (10, 100), or (12.5, 156.25); the width that creates the maximum area.
4. no zeros 5. x 5 5, 10
8. 5 ft by 5 ft, 6 ft by 6 ft, 10 ft by 10 ft, or 12.5 ft by 12.5 ft
6. 4
9. a square
7. 7.2 seconds
10. a. No dimensions work; b. 36 w 10w has no real solutions.; 6 ft by 6 ft; 2 36 w 12w has only one solution, w 6 and l 6 .; c. 2 ft by 18 ft; 36 2 w 20w has two solutions, w 2 and l 18 or w 18 and l 2 .; 25 481 ft by 25 481 ___________ ft; d. ___________
Y
2
2
2
36 w 25w has two solutions, 25 481 . w ___________ 2
2
X
Cumulative Test
8. g x has the same width and same axis of symmetry, but it opens downward and its vertex is translated 3 units up to (0, 3).
1. B
9. x 0 or x 2
3. C
Copyright © by Holt, Rinehart and Winston. All rights reserved.
285
2. J
Holt Algebra 1
