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Math 20-2: Quadratic Functions Practice Exam

Name: ___________________________ Period: _____________________ Date: ___________________________ Teacher: _____________________

Show your work in the space beside each question. Diagrams shown are not drawn to scale.

Multiple Choice

Identify the choice that best completes the statement or answers the question.

1. The relation that is a quadratic is

a. y = (x + 5)2

b. y = (2x2)(x + 1)

c. y = x3x2 + 4x + 2

d. y = 2x + 3

2. The y-intercept for y = 3x2 + 2x – 5 is

a. –5 b. 5 c. 2 d. 3

3. The x- and y-intercepts for the function f(x) =x2 – 2x – 8 are

a. no x-intercepts, y = –8 b. x = –2, x = 4, y = –8 c. x = –2, x = 2, y = –8 d. x = –4, x = 4, y = –8

4. The set of ordered pairs satisfy the function f(x) = –2x2 + 2.5x + 1 is

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Use the following information to answer the next question

1 2 3 4 5

–1 –2 –3 –4

–5 x

1 2 3 4 5

–1 –2 –3 –4 –5

y

Axis of Symmetry Vertex Domain Range

A. x = –2 (–0.25, –3.125) x R y R

B. x = –0.25 (–0.25, 3.125) x R y 3.125

C. x = –0.5 (–0.5, 3) –2.5 x 1.5 y 3

D. x = 3 (3, –0.5) –3 x 2 y 5

5. The set of data that is correct for this graph is

a. A b. B c. C d. D

6. The points (–1, 14) and (9, 14) are located on the same parabola. The equation for the axis of symmetry for this parabola is

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Use the following information to answer the next question

1 2 3 4 5

–1 –2 –3 –4

–5 x

1 2 3 4 5

–1 –2 –3 –4 –5

y

7. The correct quadratic function for this parabola is a. f(x) = (x + 1)(x + 3)

b. f(x) = (1 – x)(3 – x) c. f(x) = (x – 1)(x + 3) d. f(x) = –(x + 1)(x – 3)

Use the following information to answer the next question

x-intercepts y-intercept Axis of Symmetry Vertex A. (–0.5, 0), (1, 0) y = –2 x = 0.25 (0.25, –1.25) B. (0.5, 0), (–1, 0) y = –2 x = –0.25 (–0.25, –2.25)

C. (–0.5, 0), (1, 0) y = 0.5 x = 0.5 (0.5, 0)

D. (0.5, 0), (–1, 0) y = –0.5 x = –0.5 (–0.5, –2) 8. The set of data that is correct for the quadratic relation f(x) = 4(x – 0.5)(x + 1) is

a. A b. B c. C d. D

NR 1

The value of a, to the nearest tenth, given that (1, 8) satisfies the quadratic function f(x) = a(x + 4)2 – 7

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Use the following information to answer the next question

x-intercepts y-intercept Axis of Symmetry Vertex

A. (2, 0), (4, 0) y = 8 x = 4 (4, 48)

B. (–2, 0), (–4, 0) y = –8 x = –4 (–4, 0)

C. (–2, 0), (–4, 0) y = 8 x = –3 (–3, –1)

D. (2, 0), (4, 0) y = 8 x = 3 (3, 35)

9. The set of data that is correct for the quadratic relation f(x) = (x + 2)(x + 4) is

a. A b. B c. C. d. D

Use the following information to answer the next question

Direction parabola opens Vertex Axis of Symmetry

A. upward (–60, –45) x = –60

B. downward (60, 45) x = 60

C. upward (–45, 60) x = –45

D. downward (45, 60) x = 45

10. The set of data that is correct for the quadratic relation f(x) = (x + 45)2 + 60 is

a. A b. B c. C d. D

11. The function that has a minimum value is

a. f(x) = –3.2(x – 4.2)2 + 1.6

b. f(x) = –3(x – 7.5)2 – 2.6

c. f(x) = –2(x + 4)2 + 6

d. f(x) = 0.5(x – 2.2)2 + 6.1

12. How many zeros does f(x) = a(x – 5)2 have if a < 0?

a. It is impossible to determine. b. 1

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Use the following graph to answer the next question

1 2 3 4 5 –1 –2 –3 –4 –5 x 1 2 3 4 5 –1 –2 –3 –4 –5 y

13. The quadratic function that represents this parabola is

a. f(x) = (x + 2)2 + 1

b. f(x) =–(x – 2)2 + 1

c. f(x) = –(x + 2)2 – 1

d. f(x) =(x – 2)2 + 1

14. The equation that represents the quadratic function y = 0.5(x + 4)(x – 3) in standard form is

a. y = 0.5x2 + 0.5x – 6

b. y = 0.5x2 – 3.5x + 6

c. y = 0.5x2 – 0.5x – 6

d. y = 0.5x2 + 3.5x + 6

Use the following graph to answer the next question

1 2 3 4 5 6 7 8 9

–1 x 1 2 3 4 5 –1 –2 –3 –4 –5 y

15. The quadratic function that defines this parabola in vertex form is

a. y = (x – 8)2 – 4

b. y = 2(x – 7)2 – 3

c. y = (x – 9)2 – 4

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Written Response

1. Fill in the table for the relation y =x2 + 2x + 11.

y-intercept x-intercept(s) Axis of symmetry Maximum

Vertex Domain Range

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3. A water hose positioned from a deck and sprays water in a path modeled by y = –0.5x2 + 0.5x + 3,

where x is the horizontal distance the water travels and y in the height of the water sprayed.

 Does the parabola formed by the equation y = –0.5x2 + 0.5x + 3 have a maximum or

minimum? Justify your answers.

 Complete the table of values

x y

0 0.5 1.0 1.5 2.0 2.5 3.0

 Sketch the function

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4. Gordon and Hanna are standing 10 ft apart, playing badminton. They use a video camera to determine that the path of the birdie on one volley is defined by the function

h(x) = –0.04(x – 5)2 + 7, where x is the horizontal distance, measured in feet, from Gordon toward

Hanna.

 Determine the axis of symmetry of the parabola.

 What was the highest point of the birdie's path?

 How high was the birdie from the ground when it was 2.5 ft from Gordon?

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Practice Exam Answer Section MULTIPLE CHOICE

1. A 2. A

3. B

x-intercepts:

Therefore, x-intercepts are 4, and -2

y-intercept:

set x = 0 and solve for y y = (0)2+2(0)-8 = -8

4. A

5. B 6. B

7. D 8. B

AofS=

NR1. a 0.6

9. C 10. C 11. D 12. B 13. B 14. A

15. A

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WRITTEN RESPONSE

1. ANS:

y-intercept (0, 11)

x-intercept(s) none

Axis of symmetry x = –1

Maximum 10

Vertex (–1, 10)

Domain x R

Range y 10

2.

Therefore, y = –0.5(x – 4)(x – 12)

2 4 6 8 10 12 14

–2 –4

–6 x

2 4 6 8

–2 –4 –6 –8 –10 –12

y

3.ANS:

x y

0 3

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1 2 3 4 5 –1

–2 –3 –4

–5 x

1 2 3 4 5

–1 –2 –3 –4 –5

y

2.5 1.125

3.0 0

 3.125 m high since this is the maximum value and 3.0 meters far since this is the zero (and you can’t have

negative height or depth).

4. ANS:

a) The vertex is (5, 7), so the axis of symmetry is x = 5.

b) The vertex is (5, 7), so the highest point of the birdie's path is 7 ft.

c) Substitute 2.5 for x in the equation and solve for h(2.5).

h(2.5) = –0.04(2.5 5)2 + 7

h(2.5) = –0.04(6.25) + 7

h(2.5) = 6.75

The birdie is 6.75 ft from the ground.

d) 0 h 7; 7 is the maximum height and the minimum height is 0 (since it can’t be negative).

References

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