Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Algebra II B Quiz 4.1-4.4 Make-up

Graph each function. How is each graph a translation of f(x) = x2?

1. y = x2

− 4

a.

f(x) translated down 4 unit(s)

c.

f(x) translated up 4 unit(s)

b.

f(x) translated to the left 4 unit(s)

d.

f(x) translated to the right 4 unit(s)

Name: ________________________ ID: A

2

2. y = (x + 2)2

a.

f(x) translated to the right 2 unit(s)

c.

f(x) translated down 2 unit(s)

b.

f(x) translated to the left 2 unit(s)

d.

f(x) translated up 2 unit(s)

Name: ________________________ ID: A

3

3. y = (x + 3)2

+ 3

a.

f(x) translated up 3 unit(s) and translated

to the left 3 unit(s).

c.

f(x) translated down 3 unit(s) and

translated to the left 3 unit(s)

b.

f(x) translated up 3 unit(s) and translated

to the right 3 unit(s)

d.

f(x) translated down 3 unit(s) and

translated to the right 3 unit(s)

Name: ________________________ ID: A

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4. Identify the vertex and the axis of symmetry of the graph of the function y = 3(x + 2)2

− 3.

a. vertex: (2, 3);

axis of symmetry: x = 2

b. vertex: (–2, –3);

axis of symmetry: x = −2

c. vertex: (–2, 3);

axis of symmetry: x = −2

d. vertex: (2, –3);

axis of symmetry: x = 2

5. Identify the maximum or minimum value of the graph of the function y = 2(x − 3)2

− 2.

a. maximum value: –2

domain: all real numbers ≤ −2

range: all real numbers

b. maximum value: 2

domain: all real numbers

range: all real numbers ≤ 2

c. minimum value: 2

domain: all real numbers ≥ 2

range: all real numbers

d. minimum value: –2

domain: all real numbers

range: all real numbers ≥ −2

Name: ________________________ ID: A

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6. Which is the graph of y = −2(x − 3)2

− 5?

a. c.

b. d.

7. What steps transform the graph of y = x2 to y = 2(x + 2)

2− 5?

a. translate 2 units to the right, translate up 5 units, stretch by the factor 2

b. reflect across the x-axis, translate 2 units to the right, translate up 5

units, stretch by the factor 2

c. reflect across the x-axis, translate 2 units to the left, translate down 5

units, stretch by the factor 2

d. translate 2 units to the left, translate down 5 units, stretch by the factor 2

Name: ________________________ ID: A

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8. Use the vertex form to write the equation of the parabola.

a. y = (x + 3)2

− 2 c. y = 3(x + 3)2

− 2

b. y = 3(x − 3)2

− 2 d. y = 3(x − 3)2

+ 2

9. Suppose a parabola has vertex (–1, –7) and also passes through the point (0, –5). Write the equation of the

parabola in vertex form.

a. y = 2(x − 1)2

− 7 c. y = 2(x + 1)2

− 7

b. y = (x + 1)2

− 7 d. y = 2(x + 1)2

+ 7

10. Suppose a parabola has an axis of symmetry at x = −4, a maximum height of 3 and also passes through the point

(–3, –1). Write the equation of the parabola in vertex form.

a. y = (x + 4)2

+ 3 c. y = −4(x − 4)2

+ 3

b. y = −4(x + 4)2

+ 3 d. y = 4(x + 4)2

− 3

What are the vertex and the axis of symmetry of the equation?

11. y = 2x2

+ 32x − 14

a. vertex: ( 8, –142)

axis of symmetry: x = −142

c. vertex: ( –8, –142)

axis of symmetry: x = −142

b. vertex: ( –8, –142)

axis of symmetry: x = −8

d. vertex: ( –8, 142)

axis of symmetry: y = −8

Name: ________________________ ID: A

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12. y = −2x2

+ 20x − 14

a. vertex: ( –5, –36)

axis of symmetry: y = −5

c. vertex: ( –5, 36)

axis of symmetry: x = −5

b. vertex: ( 5, 36)

axis of symmetry: x = 5

d. vertex: ( 5, 36)

axis of symmetry: x = 36

What is the maximum or minimum value of the function?

13. y = 2x2

+ 16x − 20

14. y = −2x2

+ 28x − 2

Name: ________________________ ID: A

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What is the graph of the equation?

15. y = x2

− 4x + 5

a. c.

b. d.

Name: ________________________ ID: A

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16. y = −x2

+ 2x + 3

a. c.

b. d.

Name: ________________________ ID: A

10

17. y = 2x2

− 2x − 1

a. c.

b. d.

Name: ________________________ ID: A

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18. You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled

with the function y = −0.000425x2

+ 0.843x where x and y are in feet. How high above the river is the bridge (the

top of the arch)? How long is the section of bridge above the arch?

a. The bridge is about 418.03 ft above the river and the length of the bridge above the arch

is about 1983.53 ft

b. The bridge is about 1983.53 ft above the river and the length of the bridge above the arch

is about 418.03 ft

c. The bridge is about 1983.53 ft above the river and the length of the bridge above the arch

is about 991.76 ft

d. The bridge is about 418.03 ft above the river and the length of the bridge above the arch

is about 991.76 ft

What is the expression in factored form?

19. x2

+ 13x + 42

a. (x − 7)(x − 6) c. (x + 6)(x − 7)

b. (x + 7)(x − 6) d. (x + 6)(x + 7)

20. x2

− 10x + 21

a. (x − 3)(x − 7) c. (x + 7)(x + 3)

b. (x − 7)(x + 3) d. (x − 3)(x + 7)

21. −x2

+ 5x + 14

a. (x + 2)(x + 7) c. (x − 7)(x − 2)

b. −(x − 7)(x + 2) d. −(x − 2)(x + 7)

What is the expression in factored form?

22. 8x2

+ 4x

a. −2x(4x + 2) c. 2x(4x − 2)

b. 2(4x + 2) d. 2x(4x + 2)

Name: ________________________ ID: A

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23. 5x2

+ 35x + 60

a. 5(x − 4)(x + 3) c. 5(x − 4)(x − 3)

b. 5(x + 4)(x − 3) d. 5(x + 4)(x + 3)

24. −4x2

+ 12x + 40

a. −4(x + 5)(x + 2) c. −4(x − 5)(x + 2)

b. −4(x + 5)(x − 2) d. −4(x − 5)(x − 2)

25. 5x2

+ 27x + 28

a. (5x + 7)(x + 4) c. (x + 7)(5x + 4)

b. (5x + 7)(x − 4) d. (5x + 4)(x − 7)

26. 5x2

− 38x − 63

a. (x + 7)(5x − 9) c. (5x − 9)(x − 7)

b. (5x + 7)(x − 9) d. (5x + 7)(x + 9)

27. 4x2

− 16x + 16

a. (2x − 4)(−2x + 4) c. (2x − 4)2

b. (−2x − 4)2

d. (2x + 4)2

28. 4x2

− 8x + 4

a. (2x − 2)2

c. (2x + 2)2

b. (−2x − 2)2

d. (−2x + 2)(2x − 2)

Name: ________________________ ID: A

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29. x2

− 16

a. (x + 4)(−x − 4) c. (x + 4)(x − 4)

b. (−x + 4)(x − 4) d. (x − 4)2

30. 9x2

− 16

a. (3x − 4)2

c. (3x + 4)(3x − 4)

b. (3x + 4)(−3x − 4) d. (−3x + 4)(3x − 4)

What are the solutions of the quadratic equation?

31. x2

+ 14x = −48

a. 6, 8 c. 6, –8

b. –6, –8 d. –6, 8

32. x2

− 11x + 24 = 0

a. –8, –3 c. –8, 3

b. 8, 3 d. 8, –3

33. 2x2

+ 11x + 15 = 0

a. –3, −5

2c. −

5

2, −

2

3

b. –3, 2 d. 3, −2

3

34. 5x2

− 18x + 9 = 0

a.3

5,

5

3c. 3, 5

b. 3, 3

5d. –3,

5

3

Name: ________________________ ID: A

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35. How would you translate the graph of y = x2 to produce the graph of y = x

2+ 10?

Name: ________________________ ID: A

15

36. Graph the quadratic function. Label the vertex and axis of symmetry.

y = x2

− 2x − 4

Name: ________________________ ID: A

16

37. Find the vertex and the axis of symmetry of the parabola. y = −3x2

+ 12x − 8

38. Find the vertex of the parabola and determine if it opens up or down. y = 7 − 8x − 2x2

39. Find the vertex and the axis of symmetry of the parabola. y = 3x2

+ 12x + 9

Name: ________________________ ID: A

17

40. Graph the function. Label the vertex, axis of symmetry, and x-intercepts.

y = − x2

− 4x + 2

Find the maximum value or minimum value for the function.

41. f x( ) = −x2

+ 6x + 4

Name: ________________________ ID: A

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42. f x( ) = 4x2

+ 6x + 3

43. f x( ) = x2

+ 7x + 5

44. f x( ) = −2x2

+ 5x + 2

45. How would you translate the graph of y = x2 to produce the graph of y = x− 7( )

2?

46. How would you translate the graph of y = −x2 to produce the graph of y = − x− 6( )

2?

a. translate the graph of y = −x2

left 6 units

b. translate the graph of y = −x2

right 6 units

c. translate the graph of y = −x2

down 6 units

d. translate the graph of y = −x2

up 6 units

47. How would you translate the graph of y = x2 to produce the graph of y = x

2+ 1?

Name: ________________________ ID: A

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48. Graph the function. Label the vertex, axis of symmetry, and x-intercepts.

y = 2 x + 2( ) x + 4( )

a.

vertex: (−3, −2)

axis of symm: x = −3

x-intercepts: –4, –2

c.

vertex: (3, −2)

axis of symm: x = 3

x-intercepts: 2, 4

b.

vertex: (−3, 2)

axis of symm: x = −3

x-intercepts: –4, –2

d.

vertex: (3, 2)

axis of symm: x = 3

x-intercepts: 2, 4

Name: ________________________ ID: A

20

Write in standard form and graph.

49. y = − x − 2( )2

− 3

a. y = −x2

− 4x + 7 c. y = −x2

− 4x − 7

b. y = −x2

+ 4x − 7 d. y = −x2

+ 4x + 7

Name: ________________________ ID: A

21

50. y = x− 1( )2+ 2

a. y = −x2

− 2x+ 1 c. y = x2+ 2x+ 3

b. y = x2− 2x+ 3 d. y = −x

2+ 2x+ 1

51. Write as the product of two factors: x2

+ 3x − 40

a. x − 5( ) x + 8( ) c. x + 5( ) x − 8( )

b. x − 5( ) x − 8( ) d. x + 5( ) x + 8( )

52. What are the solutions of the equation?

x2

− 10x + 24 = 0

a. x = −1 or x = −24 c. x = −1 or x = 24

b. x = −4 or x = −6 d. x = 4 or x = 6

53. Solve using factoring: x2

− 2x − 8 = 0

a. −2, − 4 b. 2, 4 c. −2, 4 d. −4, 2

Name: ________________________ ID: A

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Find the zeros of the function.

54. y = x2

− 11x + 18

55. A restaurant has a patio that is 8 feet wide and 12 feet long. The restaurant owners want to double the area of the

patio by increasing the width and the length by the same distance x. Write an equation that x must satisfy. Can

your equation be solved by factoring? Is there a single solution or more than one solution? Explain.

56. Write as the product of two factors: 12h2

− 31h + 20

57. Write as a product of factors.

12x2

+ 25x + 12

Name: ________________________ ID: A

23

Factor the expression.

58. 5x2

− 42x + 16

Solve.

59. x2

− 6x = 0

a. 0, 6 c. –6, 6

b. 0, –6 d. 1, 6

60. 4x2

− 12x − 16 = 0

ID: A

1

Algebra II B Quiz 4.1-4.4 Make-up

Answer Section

1. A

2. B

3. A

4. B

5. D

6. D

7. D

8. C

9. C

10. B

11. B

12. B

13. minimum value: –52

range: y ≥ −52

14. maximum: 96

range: y ≤ 96

15. A

16. A

17. A

18. A

19. D

20. A

21. B

22. D

23. D

24. C

25. A

26. B

27. C

28. A

29. C

30. C

31. B

32. B

33. A

34. B

35. Move the graph of y = x2 up 10 units to get the graph of y = x

2+ 10.

ID: A

2

36.

axis of symmetry: x = 1

vertex: (1, −5)

37. Vertex: (2, 4); Axis: x = 2

38. Vertex: (-2, 15); Opens down

39. Vertex: (-2, -3); Axis: x = -2

40.

vertex: −2, 6ÊËÁÁ ˆ

¯˜̃ ; axis of symmetry: x = −2;x-intercepts at − 4.4, 0.4

41. maximum: 13

42. minimum: 0.75

43. minimum: –7.25

44. maximum: 5.125

45. translate the graph of y = x2

right 7 units

46. B

47. translate the graph of y = x2

up 1 unit

48. A

49. B

50. B

51. A

52. D

53. C

ID: A

3

54. 9, 2

55. x + 8( ) x + 12( ) = 192

Yes.

The equation to be solved is x2

+ 20x − 96 = 0. Because x2

+ 20x − 96 = x − 4( ) x + 24( ) the solutions to the

equation are x = 4 or x = −24. Since the answer cannot be negative, there is only one solution: the patio should be

increased by 4 feet in each direction.

56. 4h − 5( ) 3h − 4( )

57. y = 3x + 4( ) 4x + 3( )

58. (x − 8)(5x − 2)

59. A

60. −1, 4