Name:
.
Review for Test 9: Quadratic Functions
1. Which of the following statements about quadratic
functions are true?
I.
II.
III.
IV.
The graph can have one solution
The graph can have two solutions
The graph can have three solutions
The graph will always cross the x-axis
A. I, II and III
C. I, II and IV
B. I, II, III and IV
D. I and II
Use the graph below to answer questions #2-7
8. What is the parent function for the following equation:
𝑓(𝑥) = (𝑥 − 2)(𝑥 + 1)
A. 𝑦 = 𝑥
C. 𝑦 = √𝑥
B. 𝑦 = 𝑥 2
D. 𝑦 = |𝑥|
9. What is/are the solution(s)
to the quadratic function:
A.
B.
C.
D.
(1,0)
(1,0) and (0, −2)
(−2,0)
None
10. What is the solution set for the quadratic
function: 𝑥 2 + 8𝑥 + 12 = 0
2. What is the axis of symmetry for the graph?
A. 𝑦 = −3
C. 𝑥 = −3
B. 𝑦 = −1
D. 𝑥 = −1
3. What is the vertex?
A. (−1, −3)
C. (−3, 0)
B. (1, 0)
D. (−3, 1)
4. What is the domain for the graph?
A. 𝑦 ≥ −3
C. −∞ < 𝑥 < ∞
B. −3 ≤ 𝑥 ≤ 1
D. {−3, 1}
5. What is the range of the function?
A. 𝑦 ≥ −3
C. −∞ < 𝑦 < ∞
B. −3 ≤ 𝑦 ≤ 1
D. 𝑦 = −3
A. {12}
C. {−6, −2}
B. 𝑁𝑜𝑛𝑒
D. {2, 6}
11. What are the roots for the
quadratic function given in
the table to the right?
A.
B.
C.
D.
−3 and −2
−6 and 1
−18
None
𝒙
−6
−5
−4
−3
−2
−1
0
1
2
𝒇(𝒙)
0
−18
−30
−36
−36
−30
−18
0
24
12. The quadratic function g has an x-intercept at (4,0),
a y-intercept at (0,6), and an axis of symmetry at 𝑥 = −2.
What are the solutions
of function g?
A. (4,0) and(0,6)
6. Which of the following statements is true?
B. (0,6)
A. minimum at 𝑥 = −3
C. maximum at 𝑦 = 4
C. (−8,0), (4,0), (0,6)
B. minimum at 𝑦 = −3
D. maximum at 𝑦 = −3
7. What is y-intercept?
A. (−3, 0)
C. (−2, 0)
B. (1,0)
D. (0, −2 )
D. (−8,0) and (4,0)
13. What is the vertex of the quadratic function:
𝑓(𝑥) = 𝑥 2 + 4𝑥 − 8
A. (0, −8)
B. (−2, −12)
C. (−1, −11)
D. (−4, −8)
14. What are the zeros of the quadratic function:
𝑦 = 2𝑥 2 − 6𝑥 + 9
A. 9
C. None
B. 1 and 2
D. 5
15. Given a quadratic function has solutions at (4, 0) and
(6, 0) which of the following is one of the linear factors of
the function?
A. (𝑥 + 4)
C. (𝑥 − 2)
B. (𝑥 − 6)
D. (𝑥 + 6)
16. Which of the following represents the range of the
quadratic function 𝑓(𝑥) = 𝑥 2 + 10𝑥 + 24 ?
A. {𝑦 | 𝑦 ≥ −5}
C. {𝑦 | 𝑦 ≥ −1}
B. {𝑦 | 𝑦 ≥ −4}
D. {𝑦| − ∞ < 𝑦 < ∞}
20. Which of the following has the correct factored
form AND the correct solutions for the quadratic
equation 𝑥 2 − 2𝑥 − 3 = 0 ?
A. (𝑥 − 1)(𝑥 + 3) = 0 AND 𝑥 = −1 and 𝑥 = 3
B. (𝑥 − 1)(𝑥 + 3) = 0 AND 𝑥 = 1 and 𝑥 = −3
C. (𝑥 + 1)(𝑥 − 3) = 0 AND 𝑥 = −1 and 𝑥 = 3
D. (𝑥 + 1)(𝑥 − 3) = 0 AND 𝑥 = 1 and 𝑥 = −3
21. Which of the following quadratic functions would
have the same solutions as the graph?
A. (𝑥 − 1)(𝑥 + 4) = 0
B. (𝑥 − 1)(𝑥 − 4) = 0
C. (𝑥 + 1)(𝑥 + 4) = 0
D. (𝑥 + 1)(𝑥 − 4) = 0
17. What are the solutions to the quadratic equation
2𝑥 2 + 10𝑥 = 12 ?
A. 𝑥 = −6 and 𝑥 = 1
C. 𝑥 = −1 and 𝑥 = 6
B. 𝑥 = −6 and 𝑥 = 12
D. 𝑥 = −3 and 𝑥 = −2
22. Which of the following correctly matches the
quadratic function graphed below?
A. 𝑓(𝑥) = 𝑥 2 + 5𝑥 + 6
18. What is the solution set to the quadratic equation
(𝑥 − 2)(𝑥 + 3) = 0 ?
B. 𝑓(𝑥) = −𝑥 2 + 𝑥 + 6
A. {−2, 3}
C. {−2, −3}
D. 𝑓(𝑥) = 2 (𝑥 2 − 𝑥 − 6)
B. {2, −3}
D. {2, 3}
19. What is the equation for the axis of symmetry of the
parabola in the function below?
A.
B.
C.
D.
𝑦=1
𝑥=3
𝑦=3
𝑥=1
C. 𝑓(𝑥) = 𝑥 2 + 𝑥 − 6
1
23. Given that the solutions to a quadratic equation are
−7 𝑎𝑛𝑑 8 , which of the following could represent the
quadratic function?
A. 𝑥 2 + 𝑥 − 56
B. 𝑥 2 − 𝑥 − 56
C. 𝑥 2 + 15𝑥 + 56
D. 𝑥 2 − 15𝑥 − 56