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Use the quadratic formula to solve the equation.
49)
x2- 14x + 74 = 0
49)
A)
{12, 2}
B)
{7 ±25i}
C)
{7 +5i}
D)
{7 ±5i}
Solve the polynomial inequality and graph the solution set on a number line.
50)
4x2+ 5x -6 0
50)
A)
, 3
4
B)
-2, 3
4
C)
( , -2] 3
4,
D)
[-2, )
Solve.
51)
The average cost per unit, C(x), of producing x units of a product is given by
C(x) =450,000 +0.35x
x. How many units must be produced so that the average cost of producing
each unit does not exceed $1.85?
51)
A)
at least 400,000 units
B)
at least 300,000 units
C)
not more than 400,000 units
D)
not more than 300,000 units
Complete the square for the binomial. Then factor the resulting perfect square trinomial.
52)
x2+11x
52)
A)
22; x2+11x +22 =(x +11)2
B)
121
2; x2+11x +121
2=x +121
2
2
C)
121
4; x2+11x +121
4=x +11
2
2
D)
121
4; x2+11x -121
4=x -11
2
2
Determine whether the given quadratic function has a minimum value or maximum value. Then find the minimum or
maximum value and determine where it occurs.
53)
f(x) =4x2- 2x - 2
53)
A)
Minimum is -9
4 at x =1
4.
B)
Minimum is 1
4 at x = - 9
4.
C)
Maximum is 1
4 at x = - 9
4.
D)
Maximum is -9
4 at x =1
4.
Solve the equation by the method of your choice. Simplify solutions, if possible.
54)
2x2- 9x - 5 = 0
54)
A)
-1
2, 5
B)
1
9, -1
2
C)
{-2, 5}
D)
-1
2, 2
Solve the problem.
55)
The owner of a video store has determined that the cost C, in dollars, of operating the store is
approximately given by C(x) = 2x2-32x +500, where x is the number of videos rented daily. Find
the lowest cost to the nearest dollar.
55)
A)
$372
B)
$244
C)
$-12
D)
$628
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
22
56)
f(x) =3(x + 3)2+ 5
56)
A)
vertex: (-5, 3)
axis of symmetry: x = - 5
B)
vertex: (-3, 5)
axis of symmetry: x = - 3
C)
vertex: (5, -3)
axis of symmetry: x =5
D)
vertex: (3, 5)
axis of symmetry: x =3
23
Solve the rational inequality and graph the solution set on a real number line.
57)
1
x + 5 <6
x + 19
57)
A)
B)
-5, -11
5
C)
(-, -5) -11
5,
D)
-, -11
5 (5, )
Solve the formula for the specified variable. Assume all variables represent nonnegative numbers. If possible, simplify
radicals and rationalize denominators.
58)
V =r2h for r
58)
A)
r =V
h
B)
r =V
2h
C)
r =Vh
D)
r =Vh
h
24
Solve the rational inequality and graph the solution set on a real number line.
59)
x - 8
x + 4 > 0
59)
A)
(8, )
B)
(-, -4) (8, )
C)
(-4, 8)
D)
(-, -4)
Use the given functions to find all values of x that satisfy the required inequality.
60)
f(x) =3x2, g(x) = - 7x + 6; f(x)
g(x)
60)
A)
-3, 2
3
B)
( , -3] 2
3,
C)
[-3, )
D)
, 2
3
Solve the equation by the method of your choice. Simplify solutions, if possible.
61)
2-10x = (3x - 7)(x + 1)
61)
A)
1
5
B)
{-3, 1}
C)
{-1, 3}
D)
-1, 7
3
25
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
62)
x2-10x +25 =100
62)
A)
{-95, 105}
B)
{15}
C)
{-5, 15}
D)
{-15, 5}
Solve the equation by making an appropriate substitution.
63)
6x-2+ 7x-1+ 1 = 0
63)
A)
-1
6, -1
B)
{-1, -6}
C)
{1, 6}
D)
1
6, 1
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
64)
f(x) = - 7(x -3)2-6
64)
A)
(3, -6)
B)
(-3, -6)
C)
(-6, 3)
D)
(-7, -3)
Solve the equation by making an appropriate substitution.
65)
y -15
y
2- 12 y -15
y-28 = 0
65)
A)
B)
{- 5, - 1, 3, 15}
C)
{- 5, 3}
D)
{-2, 14}
66)
x4-29x2+100 = 0
66)
A)
{-2i, 2i, -5i, 5i}
B)
{2, 5}
C)
{-2, 2, -5, 5}
D)
{4, 25}
26
67)
x2/3 - 7x1/3 + 12 = 0
67)
A)
{27, 64}
B)
{-64, -27}
C)
{3, 4}
D)
{-4, -3}
Solve the rational inequality and graph the solution set on a real number line.
68)
-x +3
x -2 0
68)
A)
[2, 3]
B)
(-, 2) [3, )
C)
(2, 3]
D)
(-, 3]
Solve the quadratic equation by completing the square.
69)
49x2+ 84x + 11 = 0
69)
A)
-1
49 , -11
49
B)
-11
49 , 22
49
C)
1
7, 11
7
D)
-1
7, -11
7
27
Solve the polynomial inequality and graph the solution set on a number line.
70)
(x - 9)(x + 6) > 0
70)
A)
(-, -9) (6, )
B)
(-6, 9)
C)
(-, -6) (9, )
D)
(-6, )
Use the quadratic formula to solve the equation.
71)
16x2+ 1 =5x
71)
A)
5
32 ± i 39
32
B)
-5±39
32
C)
-5
32 ± i 39
32
D)
5±39
32
Solve the quadratic equation by completing the square.
72)
x2+ 5x - 5 = 0
72)
A)
{-5±3 5}
B)
-5+3 5
2
C)
-5±3 5
2
D)
5±3 5
2
28
Use the quadratic formula to solve the equation.
73)
x2+7x +2= 0
73)
A)
-7±41
14
B)
-7±57
2
C)
7±41
2
D)
-7±41
2
Solve the problem.
74)
The formula P =0.64x2-0.047x +3 models the approximate population, P, in thousands, for a
species of fish in a local pond, x years after 2010. During what year will the population reach 94.596
thousand fish?
74)
A)
2023
B)
2021
C)
2024
D)
2022
Solve the equation by making an appropriate substitution.
75)
x-2- 10x-1= - 20
75)
A)
-5±5
20
B)
5±5
30
C)
5± 2 5
20
D)
5±5
20
Solve.
76)
The perimeter of a rectangle is 62 feet. Describe the possible length of a side if the area of the
rectangle is not to exceed 198 square feet.
76)
A)
The length of the shortest side cannot exceed 22 feet.
B)
The length of the shortest side cannot exceed 9 feet.
C)
The length of the shortest side must be at least 9 feet.
D)
The length of the shortest side must be at least 22 feet.
Solve the polynomial inequality and graph the solution set on a number line.
77)
4x2+ 15x -4< 0
77)
A)
, 1
4
B)
(-4, )
C)
-4, 1
4
D)
( , -4) 1
4,
30
Solve the rational inequality and graph the solution set on a real number line.
78)
x + 19
x + 5 <6
78)
A)
B)
-, -11
5 (5, )
C)
(-, -5) -11
5,
D)
-5, -11
5
Solve.
79)
A guy wire is to be attached to the top of a 29-foot antenna. If the wire must be anchored 29 feet
from the base of the antenna, what length of wire is required?
79)
A)
29 ft
B)
29 2 ft
C)
1682 ft
D)
58 ft
Sketch the graph of the quadratic function. Identify the vertex, intercepts, and the equation for the axis of symmetry.
31
80)
f(x) =3-x2+ 2x
80)
A)
vertex: (- 1, 4)
x-intercepts: (-3, 0) and (1, 0)
y-intercept: (0, 3)
axis of symmetry: x = - 1
B)
vertex: (1, 4)
x-intercepts: (-1, 0) and (3, 0)
y-intercept: (0, 3)
axis of symmetry: x =1
C)
vertex: (1, - 4)
x-intercepts: (-1, 0) and (3, 0)
y-intercept: (0, 3)
axis of symmetry: x =1
D)
vertex: (1, 4)
x-intercepts: (-3, 0) and (1, 0)
y-intercept: (0, 3)
axis of symmetry: x =1
32
Use the discriminant to determine the number and type of solutions for the given equation.
81)
4+ 8x2= - 6x
81)
A)
two real rational solutions
B)
two imaginary solutions
C)
two real irrational solutions
D)
one (repeated) real rational solution
Solve the rational inequality and graph the solution set on a real number line.
82)
x
x +7> 0
82)
A)
(0, )
B)
(-, -7) (0, )
C)
(-7, 0]
D)
(-, -7] [0, )
Use the quadratic formula to solve the equation.
83)
x2+ 14x + 26 = 0
83)
A)
{7 +23}
B)
{7 ±26}
C)
{-14 +26}
D)
{-7±23}
33
Solve.
84)
A supporting wire is to be attached to the top of a 37-foot antenna. If the wire must be anchored 37
feet from the base of the antenna, what length of wire is required?
84)
A)
74 ft
B)
37 2 ft
C)
2738 ft
D)
37 ft
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
85)
x2+ 16x
85)
A)
8; x2+ 16x +8= (x +64)2
B)
16; x2+ 16x +16 = (x +256)2
C)
64; x2+ 16x +64 = (x +8)2
D)
256; x2+ 16x +256 = (x +16)2
Use the discriminant to determine the number and type of solutions for the given equation.
86)
8x2= - 5x - 5
86)
A)
two real irrational solutions
B)
two imaginary solutions
C)
two real rational solutions
D)
one (repeated) real rational solution
Write a quadratic equation in standard form with the given solution set.
87)
{-6i, 6i}
87)
A)
x2+36 = 0
B)
x2-36 = 0
C)
x2-12x -36 = 0
D)
x2+12x +36 = 0
Solve the problem.
88)
The daily profit in dollars of a specialty cake shop is described by the function
P(x) = - 6x2+264x -2304, where x is the number of cakes prepared in one day. The maximum
profit for the company occurs at the vertex of the parabola. How many cakes should be prepared
per day in order to maximize profit?
88)
A)
2904 cakes
B)
44 cakes
C)
484 cakes
D)
22 cakes
Write a quadratic equation in standard form with the given solution set.
89)
{-10, 5}
89)
A)
x2- 50x - 5 = 0
B)
x2+ 50x - 5 = 0
C)
x2+ 5x - 50 = 0
D)
x2- 5x - 50 = 0
Solve the problem.
90)
If g(x) = (x + 3)2, find all values of x for which g(x) =11.
90)
A)
3±11
B)
-3±11
C)
±11
3
D)
±11
Use the discriminant to determine the number and type of solutions for the given equation.
91)
x2- 4x + 3 = 0
91)
A)
two real rational solutions
B)
two imaginary solutions
C)
one (repeated) real rational solution
D)
two real irrational solutions
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
92)
f(x) = (x - 1)2- 1
92)
A)
(1, -1)
B)
(0, -1)
C)
(-1, 0)
D)
(1, 1)
Solve.
93)
A 30-foot pole is supported by two wires that extend from the top of the pole to points that are
each 5 feet from the base of the pole. Find the total length of the two wires.
93)
A)
1850 ft
B)
10 37 ft
C)
70 ft
D)
537 ft
Solve the equation by making an appropriate substitution.
94)
x-2+ 10x-1+9= 0
94)
A)
-1
9, -1
B)
{-1, -9}
C)
1
9, 1
D)
{1, 9}
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
95)
f(x) =x2- 4x + 9
95)
A)
(2, -3)
B)
(-4, 41)
C)
(-2, 21)
D)
(2, 5)
Solve the problem.
96)
An object is propelled vertically upward from the top of a 32-foot building. The quadratic function
s(t) = - 16t2+240t +32 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.
96)
A)
0.1 sec
B)
2 sec
C)
7.5 sec
D)
15.1 sec
Find the intercepts of the quadratic function.
97)
f(x) =x2+ 4x - 7
97)
A)
x-intercepts: (-2 ±11, 0)
y-intercept: (0, -7)
B)
x-intercepts: none
y-intercept: (0, 7)
C)
x-intercepts: (-4, 0) and (3, 0)
y-intercept: (0, -12)
D)
x-intercept: (4, 0)
y-intercept: (0, -7)
Solve the problem.
98)
An object is propelled vertically upward from the top of a 32-foot building. The quadratic function
s(t) = - 16t2+160t +32 models the ball's height above the ground, s(t), in feet, t seconds after it was
thrown. How many seconds does it take until the object finally hits the ground? Round to the
nearest tenth of a second if necessary.
98)
A)
0.2 sec
B)
2 sec
C)
10.2 sec
D)
5 sec
Use the quadratic formula to solve the equation.
99)
x2- 15x + 56 = 0
99)
A)
{-8, 7}
B)
{56, 0}
C)
{-8, -7}
D)
{8, 7}
Solve the equation by the method of your choice. Simplify solutions, if possible.
100)
(x +3)(x -4) =2
100)
A)
1±57
2
B)
1
2± i 57
2
C)
-1
2± i 57
2
D)
-1±57
2
37
Solve the quadratic equation by completing the square.
101)
x2+ x + 3 = 0
101)
A)
1 ±i11
2
B)
-1 ±11
2
C)
1 ±11
2
D)
-1 ±i11
2
Solve.
102)
The formula F =0.04x2+17 models the percentage of female tenured faculty, F, at State University
x years after 2010. According to the formula, in what year will the percentage of female tenured
faculty reach 44.04?
102)
A)
2036
B)
2038
C)
2037
D)
2035
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
103)
f(x) =3x2+ 6x - 9
103)
A)
(2, 15)
B)
(1, 0)
C)
(-2, -3)
D)
(-1, -12)
Solve the problem.
104)
Among all pairs of numbers whose sum is 46, find a pair whose product is as large as possible.
104)
A)
45 and 1
B)
23 and 23
C)
25 and 21
D)
11.5 and 11.5
Find the range of the quadratic function.
105)
y +4=(x + 2)2
105)
A)
( , 4]
B)
[4, )
C)
( , 2]
D)
[- 4, )
38
Solve the rational inequality and graph the solution set on a real number line.
106)
6
x -1< 1
106)
A)
(-, 1] [7, )
B)
(-, 1)
C)
(-, 1) (7, )
D)
(1, 7)
Solve the problem.
107)
The hypotenuse of a right triangle is 5 feet long. One leg of the triangle is 3 feet longer then the
other leg. Find the perimeter of the triangle.
107)
A)
-3
2+41
2 ft
B)
(41 -5) ft
C)
3
2+41
2 ft
D)
(41 +5) ft
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
108)
(x + 3)2=15
108)
A)
{3 ±15}
B)
{±15}
C)
{-3±15}
D)
±15
3
39
Find the range of the quadratic function.
109)
f(x) = x2+ 4
109)
A)
[0, )
B)
[4, )
C)
[-4, )
D)
( , 4]
Solve the problem.
110)
You have 76 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence
the side along the river, find the length and width of the plot that will maximize the area.
110)
A)
length: 57 ft, width: 19 ft
B)
length: 38 ft, width: 38 ft
C)
length: 19 ft, width: 19 ft
D)
length: 38 ft, width: 19 ft
Solve the quadratic equation by completing the square.
111)
x2- 2x -5
4= 0
111)
A)
5
2, 1
2
B)
-5
2, 1
2
C)
5
2, -1
2
D)
-5
2, -1
2
Write a quadratic equation in standard form with the given solution set.
112)
{3, 6}
112)
A)
x2-18x +9= 0
B)
x2+9x +18 = 0
C)
x2-9x +18 = 0
D)
x2+18x +9= 0
113)
{-5 6, 5 6}
113)
A)
x2-150 = 0
B)
x2-10 6x +150 = 0
C)
x2+10 6x -150 = 0
D)
x2+150 = 0
