ALGEBRA II
TEST 2: QUADRATIC FUNCTIONS
PRACTICE MATERIALS
SEMESTER 1
NAME:_____________________________
DATE:________________PERIOD_______
NON-CALCULATOR SECTION
_______1. What is the product of 𝑎 + 𝑏𝑖 𝑎𝑛𝑑 𝑎 − 𝑏𝑖 written in standard form?
(A)
𝑎2 − 𝑏 2
(B)
𝑎2 + 𝑏𝑖
(C)
𝑎2 − 𝑏 2 𝑖
(D)
𝑎2 + 𝑏 2
________2. Simplify (1- 3i) - (-3+ 7i) .
(A)
4 -10i
(B)
4 + 4i
(C)
18 +16i
(D)
-2 + 4i
________3. Find the domain and range of the function shown below.
(A) D: all real numbers R: all real numbers
(B) D: all real numbers R: 𝑦 ≥ 1
(C) D: all real numbers
R: 𝑦 ≤ 1
(D) D: all real numbers
R: 𝑦 < 1
________4. Which of the following is not true of the graph of the function 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 7?
(A) It can be written in vertex form: 𝑓(𝑥) = (𝑥 + 1)2 − 8.
(B) The axis of symmetry is 𝑥 = −1.
(C) The y-intercept is -7.
(D) The maximum value is -6.
Page 1 of 8
ALGEBRA II
TEST 2: QUADRATIC FUNCTIONS
PRACTICE MATERIALS
SEMESTER 1
NAME:_____________________________
DATE:________________PERIOD_______
________5. If 𝑥 2 + 6𝑥 − 2 = (𝑥 − ℎ)2 + 𝑘, what is the value of k?
(A)
−11
(B)
−7
(C)
7
(D)
11
________6. Find the roots of 4𝑥 2 + 6 = 0.
6
2
(A)
x
(B)
x
(C)
x
i 6
2
(D)
x
6
4
6
4
________7. Factor 9 x2  121 .
(A)
(3x  11)(3 x  11)
(B)
(3x  11)(3 x  11)
(C)
(3x  11i)(3x  11i)
(D)
(3x  11i)(3x  11i)
________8. Solve x2  25  0 over the set of complex numbers.
(A)
25i
(B)
5
(C)
5i
(D)
25
Page 2 of 8
ALGEBRA II
TEST 2: QUADRATIC FUNCTIONS
PRACTICE MATERIALS
SEMESTER 1
NAME:_____________________________
DATE:________________PERIOD_______
________9. Function A and Function B are continuous quadratic functions.
Function A
Function B
f ( x)  x 2  x  6
Which function has a greater positive x-intercept?
(A)
Function A
(B)
Function B
________10. Solve the equation 6x2  24x  126 by factoring.
(A)
x  7 or x  3
(B)
x  7 or x  3
(C)
x  7
(D)
x3
________11. Which of the following functions has its vertex above the x-axis?
(A) 𝑓(𝑥) = 2(𝑥 − 5)2 − 2
1
(B) 𝑓(𝑥) = 2 (𝑥 + 2)2 − 5
(C) 𝑓(𝑥) = −3𝑥 2
(D) 𝑓(𝑥) = 4(𝑥 − 8)2 + 3
Page 3 of 8
ALGEBRA II
TEST 2: QUADRATIC FUNCTIONS
PRACTICE MATERIALS
SEMESTER 1
NAME:_____________________________
DATE:________________PERIOD_______
________12. What is the equation of the parabola shown?
(A)
y  4 x 2
(B)
y  2 x 2
(C)
1
y   x2
2
(D)
1
y   x2
4
________13. What is the solution set of y 2  2 y  3 y  14 ?
(A)
y7
(B)
y  2 or y  7
(C)
7  y  2
(D)
2  y  7
Page 4 of 8
ALGEBRA II
TEST 2: QUADRATIC FUNCTIONS
PRACTICE MATERIALS
SEMESTER 1
NAME:_____________________________
DATE:________________PERIOD_______
________14. Which of the following quadratic equations has no real roots?
(A)
2 x2  7 x  9  0
(B)
2 x2  7 x
(C)
2 x2  7 x  9  0
(D)
2 x2  7 x  9  0
________15. Find the vertex of y = x 2 + 2x - 3 and state if it is a maximum or a minimum.
(A)
(-1, -4); maximum
(B)
(-1, -4); minimum
(C)
(-4, -1); maximum
(D)
(-4, -1); minimum
________16. For what values of c will 3x2  2 x  c  0 have exactly one distinct real root?
(A)

3
2
(B)

1
3
(C)
1
3
(D)
2
3
Page 5 of 8
ALGEBRA II
TEST 2: QUADRATIC FUNCTIONS
PRACTICE MATERIALS
SEMESTER 1
NAME:_____________________________
DATE:________________PERIOD_______
________17. Solve the equation by using the quadratic formula.
2 x2  5x  3  0
1
(A)
𝑥=−
(B)
x = 1 or x = -6
(C)
x=
1
or x = -3
2
(D)
x
1
or x  1
3
2
or 𝑥 = 3
________18. Several values of the quadratic function f ( x) are given in the table.
x
f ( x)
4
2
0
96
24
0
4
9
96
486
The function g ( x ) is given by g ( x)  ( x  2) 2  3 . Which function has the greater maximum
for which value of x ?
(A)
f ( x); for x  0
(B)
f ( x); for x  6
(C)
g ( x); for x  2
(D)
g ( x); for x  3
Page 6 of 8
ALGEBRA II
TEST 2: QUADRATIC FUNCTIONS
PRACTICE MATERIALS
SEMESTER 1
NAME:_____________________________
DATE:________________PERIOD_______
________19. Use the graph provided to choose the best description of what the graph represents.
Height (ft)
Time (s)
(A)
A ball is dropped from a height of 42 feet and lands on the ground after 3 seconds.
(B)
A ball is dropped from a height of 42 feet and lands on the ground after 1.5 seconds.
(C)
A ball is shot up in the air and reaches a height of 42 feet after 1 second.
(D)
A ball is shot up in the air, reaches a height of 42 feet, and lands on the ground after
1.5 seconds.
_________20. The axis of symmetry for a quadratic function is the line 𝑥 = −2. Use the table
below to approximate one of the x-intercepts. In what interval is the other xintercept?
𝑥
𝑦
(A) Between -2 and 1
−5
−4
(B) Between -1 and 0
(C) Between 0 and 1
−4
1
(D) Between 1 and 2
−3
4
−2
5
Page 7 of 8
ALGEBRA II
TEST 2: QUADRATIC FUNCTIONS
PRACTICE MATERIALS
SEMESTER 1
NAME:_____________________________
DATE:________________PERIOD_______
CONSTRUCTED RESPONSE.: Calculators OK.
Problem Solving. Make sure to show your work. If you solved algebraically, write your
equations/steps neatly and clearly. If you solved graphically, sketch the graph and
write your analysis and brief explanation. Write your answers in complete sentences.
21. The height of Carl, the human cannonball, is given by h(t )  16t 2  56t  40 where h is in
feet and t is in seconds after the launch.
a) What was his height at the launch?
b) What was his initial velocity?
c) How many seconds after the launch will he reach the maximum height?
d) What is his maximum height?
e) How long before he lands in the safety net, 8 feet above the ground?
Page 8 of 8