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Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the graph with its function using the x-intercepts.
1)
1)
A)
f(x) =x1/3 +8x1/6 -9
B)
f(x) =x1/3 -8x1/6 +9
C)
f(x) =x1/3 +8x1/6 +9
D)
f(x) =x1/3 -8x1/6 -9
2)
2)
A)
f(x) =x1/2 + 2x1/4 + 1
B)
f(x) =x1/2 +13x1/4 -14
C)
f(x) =x1/2 + 2x1/4 - 1
D)
f(x) =x1/2 -13x1/4 -14
The graph of a quadratic function is given. Choose the function's equation.
3)
3)
A)
f(x) =(x +3)2-3
B)
f(x) =(x -3)2-3
C)
f(x) =(x +3)2+3
D)
f(x) =(x -3)2+3
Match the graph with its function using the x-intercepts.
4)
4)
A)
f(x) =(x - 4)2- 10(x - 4) + 21
B)
f(x) =(x - 4)2- 2(x - 4) - 3
C)
f(x) =(x - 4)2+ 10(x - 4) + 21
D)
f(x) =(x - 4)2+ 2(x - 4) - 3
The graph of a quadratic function is given. Choose the function's equation.
5)
5)
A)
f(x) =x2+3
B)
f(x) =x2+6x +9
C)
f(x) =x2-6x +9
D)
f(x) =x2-3
Match the graph with its function using the x-intercepts.
6)
6)
A)
f(x) = 6x-2- 5x-1- 1
B)
f(x) = 6x-2- 5x-1+ 1
C)
f(x) = 6x-2+ 5x-1- 1
D)
f(x) = 6x-2+ 5x-1+ 1
The graph of a quadratic function is given. Choose the function's equation.
7)
7)
A)
f(x) =(x -1)2-1
B)
f(x) =(x -1)2+1
C)
f(x) =(x +1)2-1
D)
f(x) =(x +1)2+1
8)
8)
A)
f(x) =x2-3
B)
f(x) =x2+6x +9
C)
f(x) =x2-6x +9
D)
f(x) =x2+3
Match the graph with its function using the x-intercepts.
9)
9)
A)
f(x) =x-2-x-1+ 2
B)
f(x) =x-2-x-1- 2
C)
f(x) =x-2+x-1- 2
D)
f(x) =x-2+x-1+ 2
The graph of a quadratic function is given. Choose the function's equation.
10)
10)
A)
f(x) =(x -2)2+2
B)
f(x) =(x -2)2-2
C)
f(x) =(x +2)2+2
D)
f(x) =(x +2)2-2
5
11)
11)
A)
f(x) =x2-2x +1
B)
f(x) =x2+1
C)
f(x) =x2-1
D)
f(x) =x2+2x +1
Match the graph with its function using the x-intercepts.
12)
12)
A)
f(x) =x4-25x2+144
B)
f(x) =x4+25x2-12
C)
f(x) =x4-25x2+12
D)
f(x) =x4+25x2+144
The graph of a quadratic function is given. Choose the function's equation.
13)
13)
A)
f(x) =x2+6x +9
B)
f(x) =x2-3
C)
f(x) =x2+3
D)
f(x) =x2-6x +9
14)
14)
A)
f(x) =(x +2)2-2
B)
f(x) =(x -2)2-2
C)
f(x) =(x -2)2+2
D)
f(x) =(x +2)2+2
Match the graph with its function using the x-intercepts.
15)
15)
A)
f(x) =x4+5x2-4
B)
f(x) =x4+5x2+4
C)
f(x) =x4-5x2+4
D)
f(x) =x4-5x2-4
The graph of a quadratic function is given. Choose the function's equation.
16)
16)
A)
f(x) = - x2+2x +1
B)
f(x) = - x2-2x -1
C)
f(x) = - x2+1
D)
f(x) = - x2-1
Match the graph with its function using the x-intercepts.
17)
17)
A)
f(x) =x-2- 2x-1- 3
B)
f(x) =x-2+ 2x-1- 3
C)
f(x) =x-2- 2x-1+ 3
D)
f(x) =x-2+ 2x-1+ 3
18)
18)
A)
f (x) =x4- 2x2- 1
B)
f (x) =x4+ 2x2- 1
C)
f (x) =x4+ 2x2+ 1
D)
f (x) =x4- 2x2+ 1
19)
19)
A)
f(x) =2(x - 1)2+ 3(x - 1) - 5
B)
f(x) =2(x + 1)2+ 3(x + 1) - 5
C)
f(x) =2(x - 1)2- 3(x - 1) - 5
D)
f(x) =2(x + 1)2- 3(x + 1) - 5
The graph of a quadratic function is given. Choose the function's equation.
20)
20)
A)
f(x) = - x2+6x +9
B)
f(x) = - x2-3
C)
f(x) = - x2+3
D)
f(x) = - x2-6x -9
Solve the equation by the method of your choice. Simplify solutions, if possible.
21)
(x + 1)(2x - 2) =9(x - 1) - 2
21)
A)
- 3, -3
2
B)
9±317
4
C)
-9±317
4
D)
3
2, 3
Solve the polynomial inequality and graph the solution set on a number line.
22)
x2+ 14x + 49 0
22)
A)
( , )
B)
( , -7]
C)
D)
[-7, )
D)
Solve the problem.
23)
Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in 2 hours.
The larger pipe can fill the pool in 4 hours less time than the smaller pipe can alone. Find the time
to the nearest tenth of an hour it takes for the smaller pipe working alone to fill the pool.
23)
A)
2.8 hr
B)
6.9 hr
C)
6.8 hr
D)
2.9 hr
Find the range of the quadratic function.
24)
f(x) = - x2+ 12x - 7
24)
A)
[6, )
B)
( , 6]
C)
[29, )
D)
( , 29]
Solve the rational inequality and graph the solution set on a real number line.
25)
24 -4x
7x +3 0
25)
A)
-3
7, 6
B)
-, -3
7 [6, )
C)
-, -3
7 [6, )
D)
[6, )
Solve the problem.
26)
The owner of a video store has determined that the profits P of the store are approximately given
by P(x) = - x2+20x +71, where x is the number of videos rented daily. Find the maximum profit to
the nearest dollar.
26)
A)
$271
B)
$200
C)
$171
D)
$100
Solve.
27)
The annual strawberry yield (in bushels per acre) for a farm in Springfield is given by the equation
y =9x2+31, where x = 0 represents 2010. Assume this trend continues and predict the year in
which the Springfield farm's strawberry yield will be 607 bushels per acre.
27)
A)
2017
B)
2020
C)
2019
D)
2018
Solve the quadratic equation by completing the square.
28)
5x2- 2x -4= 0
28)
A)
-1 ±21
5
B)
1 ±21
5
C)
5±21
25
D)
-4, 22
5
Solve the problem.
29)
A ball is thrown downward with an initial velocity of 42 meters per second from a cliff that is
100 meters high. The height of the ball is given by the quadratic equation h = - 4.9t2-42t +160
where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the
ball will be 60 meters from the ground. Round your answer to the nearest tenth of a second.
29)
A)
1.8 sec
B)
2.0 sec
C)
2.9 sec
D)
1.9 sec
Solve.
30)
An arrow is fired straight up from the ground with an initial velocity of 192 feet per second. Its
height, s(t), in feet at any time t is given by the function s(t) = - 16t2+192t. Find the interval of time
for which the height of the arrow is greater than 176 feet.
30)
A)
between 1 and 11 sec
B)
before 11 sec
C)
before 1 sec or after 11 sec
D)
after 1 sec
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
13
31)
f(x) = (x - 5)2+ 1
31)
A)
vertex (-5, 1)
axis of symmetry: x = - 5
B)
vertex (1, 5)
axis of symmetry: x =1
C)
vertex (5, 1)
axis of symmetry: x =5
D)
vertex (-1, -5 )
axis of symmetry: x = - 1
14
Solve the problem.
32)
Let f(x) =(x2-4x)2-17(x2-4x). Find all x such that f(x) = - 60.
32)
A)
6, 5
B)
- 2, - 1, 6, 5
C)
- 2, - 1, 12, 5, 6, 5
D)
12, 5
Solve.
33)
The distance, s(t), in feet traveled by a freely falling object is given by the function s(t) = 16t2, where
t is time in seconds. Use this formula to find the time it would take for an object to fall to the
ground from a cliff that is 1600 feet high.
33)
A)
9 sec
B)
10 sec
C)
100 sec
D)
11 sec
Solve the problem.
34)
April shoots an arrow upward into the air at a speed of 32 feet per second from a platform that is 32
feet high. The height of the arrow is given by the function h(t) = - 16t2+32t +32, where t is the time
is seconds. What is the maximum height of the arrow?
34)
A)
31 ft
B)
48 ft
C)
16 ft
D)
32 ft
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
35)
(x - 4)2=9
35)
A)
{7, 1}
B)
{3, -3}
C)
{13}
D)
{1, -7}
Sketch the graph of the quadratic function. Identify the vertex, intercepts, and the equation for the axis of symmetry.
15
36)
f(x) = - 2x2+ 16x - 37
36)
A)
vertex (-4, -5)
x-intercepts: none
y-intercept 0, - 13
axis of symmetry: x = - 4
B)
vertex (4, -5)
x-intercepts: none
y-intercept: 0, - 13
axis of symmetry: x =4
C)
vertex (-4, -5)
x-intercepts: none
y-intercept (0, -37)
axis of symmetry: x = - 4
D)
vertex: (4, -5)
x-intercepts: none
y-intercept: (0, -37)
axis of symmetry: x =4
16
Solve.
37)
A rectangular park is 15 km long and 8 km wide. How long is a pedestrian route that runs
diagonally across the park?
37)
A)
34 km
B)
578 km
C)
46 km
D)
17 km
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
38)
f(x) = - (x + 1)2+ 9
38)
A)
vertex: (- 1, 9)
axis of symmetry: x = - 1
B)
vertex: (- 1, 9)
axis of symmetry: x = - 1
C)
vertex: (1, - 9)
axis of symmetry: x =1
D)
vertex: (1, 9)
axis of symmetry: x =1
17
Solve the problem.
39)
An object is propelled vertically upward from the top of a 160-foot building. The quadratic
function s(t) = - 16t2+112t +160 models the ball's height above the ground, s(t), in feet, t seconds
after it was thrown. After how many seconds does the object reach its maximum height? Round to
the nearest tenth of a second if necessary.
39)
A)
3.5 sec
B)
2 sec
C)
8.2 sec
D)
1.2 sec
Solve the equation by the method of your choice. Simplify solutions, if possible.
40)
(2x - 1)2=49
40)
A)
{3, -4}
B)
{8, -6}
C)
{4, -3}
D)
{6, -8}
Complete the square for the binomial. Then factor the resulting perfect square trinomial.
41)
x2-5x
41)
A)
25
4; x2-5x -25
4=x -5
2
2
B)
25
4; x2-5x +25
4=x -5
2
2
C)
25; x2-5x +25 =(x -5)2
D)
5
2; x2-5x +5
2=x -5
2
2
Solve the problem.
42)
The profit that the vendor makes per day by selling x pretzels is given by the function
P(x) = - 0.002x2+1.4x - 350. Find the number of pretzels that must be sold to maximize profit.
42)
A)
0.7 pretzels
B)
-105 pretzels
C)
700 pretzels
D)
350 pretzels
43)
Let f(y) =y -12
y
2- 3 y -12
y. Find all y such that f(y) =4.
43)
A)
-1, 4
B)
- 4, 3
C)
D)
- 4, - 2, 3, 6
Solve.
44)
The total profit function P(x) for a company producing x thousand units is given by
P(x) = - 3x2+ 54x - 195. Find the values of x for which the company makes a profit. [Hint: The
company makes a profit when P(x) > 0.]
44)
A)
x is less than 13 thousand units
B)
x is between 5 thousand units and 13 thousand units
C)
x is less than 5 thousand units or greater than 13 thousand units
D)
x is greater than 5 thousand units
Without solving the given quadratic equation, determine the number and type of solutions.
45)
x2+ 6x - 1 = 0
45)
A)
two real rational solutions
B)
one (repeated) real rational solution
C)
two imaginary solutions
D)
two real irrational solutions
19
Solve the polynomial inequality and graph the solution set on a number line.
46)
x2+ 14x + 49 < 0
46)
A)
( , )
B)
(-7, )
C)
D)
( , -7)
Solve the problem.
47)
You have 312 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle
that maximize the enclosed area.
47)
A)
80 ft by 76 ft
B)
156 ft by 39 ft
C)
156 ft by 156 ft
D)
78 ft by 78 ft
48)
A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to
form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and
allow the greatest amount of water to flow.
48)
A)
5.5 in.
B)
4 in.
C)
4.5 in.
D)
5 in.
