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Solve the problem.
114)
You have 116 feet of fencing to enclose a rectangular region. What is the maximum area?
114)
A)
13,456 sq ft
B)
837 sq ft
C)
841 sq ft
D)
3364 sq ft
Solve the equation by making an appropriate substitution.
115)
x4- 3x2-54 = 0
115)
A)
{3, i 6}
B)
{-6, 6, -3i, 3i}
C)
{-3, 3, -i 6, i 6}
D)
{-9, 6}
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
116)
f(x) = x2- 2
116)
A)
(2, 0)
B)
(0, 2)
C)
(1, 0)
D)
(0, -2)
Find the axis of symmetry of the parabola defined by the given quadratic function.
117)
f(x) =6x2- 12x + 3
117)
A)
x =2
B)
x = - 1
C)
x = - 3
D)
x =1
Solve the problem.
118)
Let f(x) =x
x -2+15 and g(x) =8x
x -2. Find all x such that f(x) = g(x).
118)
A)
5
2, 3
B)
25
12 , 9
4
C)
5, 3
D)
-25
12 , -9
4
119)
Suppose that an open box is to be made from a square sheet of cardboard by cutting out 3-inch
squares from each corner as shown and then folding along the dotted lines. If the box is to have a
volume of 243 cubic inches, find the original dimensions of the sheet of cardboard.
119)
A)
3 in. by 3 3 in.
B)
15 in. by 15 in.
C)
9 3 in. by 9 3 in.
D)
9 in. by 9 in.
Solve the formula for the specified variable. Assume all variables represent nonnegative numbers. If possible, simplify
radicals and rationalize denominators.
120)
V =s2h
3 for s
120)
A)
s =3Vh
h
B)
s =3V
h
C)
s =3Vh
D)
s =3V
2h
Solve the polynomial inequality and graph the solution set on a number line.
121)
2x2+ 7x -15
0
121)
A)
-5, 3
2
B)
( , -5] 3
2,
C)
, 3
2
D)
[-5, )
Find the intercepts of the quadratic function.
122)
f(x) = - x2- 2x +8
122)
A)
x-intercepts: (-2, 0) and (4, 0)
y-intercept: (0, 8)
B)
x-intercepts: (-2, 0) and (4, 0)
y-intercept: (0, -8)
C)
x-intercepts: (-4, 0) and (2, 0)
y-intercept: (0, 8)
D)
x-intercepts: (-4, 0) and (2, 0)
y-intercept: (0, -8)
Solve the equation by the method of your choice. Simplify solutions, if possible.
123)
7x2-5x -2= 0
123)
A)
5±9
14
B)
5±61
14
C)
5
14 ± i 61
14
D)
-5±61
14
Sketch the graph of the quadratic function. Identify the vertex, intercepts, and the equation for the axis of symmetry.
43
124)
f(x) =x2+ 4x - 7
124)
A)
vertex: (-2, 3)
x-intercepts: none
y-intercept: (0, 7)
axis of symmetry: x = - 2
B)
vertex: -1
2, -12 1
4
x-intercepts: (-4, 0) and (3, 0)
y-intercept: (0, -12)
axis of symmetry: x = - 1
2
C)
vertex: (4, 0)
x-intercept: (4, 0)
y-intercept: (0, 7)
axis of symmetry: x = 4
D)
vertex: (-2, -11)
x-intercepts: (-2 ±11, 0)
y-intercept: (0, -7)
axis of symmetry: x = - 2
Use the quadratic formula to solve the equation.
125)
4x2= - 12x - 3
125)
A)
-3±6
2
B)
-3±3
2
C)
-12 ±6
2
D)
-3±6
8
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.
126)
f(x) = - x2- 2x + 1
126)
A)
Minimum is - 1 at x =2.
B)
Maximum is - 1 at x =2.
C)
Maximum is 2 at x = - 1.
D)
Minimum is 2 at x = - 1.
Solve the equation by making an appropriate substitution.
127)
x-2-x-1-12 = 0
127)
A)
{4, -3}
B)
-1
4, 1
3
C)
1
4, -1
3
D)
{-4, 3}
D)
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
128)
14x2-3= 0
128)
A)
±14
3
B)
±3
14
C)
±14
42
D)
±42
14
Write a quadratic equation in standard form with the given solution set.
129)
{-5, 5}
129)
A)
x2+ 2 5x -5= 0
B)
x2+5= 0
C)
x2-5= 0
D)
x2- 2 5x +5= 0
Solve the equation by the method of your choice. Simplify solutions, if possible.
130)
8
x2- 5x + 6
=2x
x - 3 -x
x - 2
130)
A)
-1
2± i 33
2
B)
1±33
2
C)
-1±33
2
D)
1
2± i 33
2
Use the given functions to find all values of x that satisfy the required inequality.
131)
f(x) =x
x +4, g(x) =2; f(x) g(x)
131)
A)
(-, -8] (-4, )
B)
(-, -4) [0, )
C)
(-4, 8]
D)
[-8, -4)
Solve the problem.
132)
The bar graph shows the percentage of students at State University that owned portable MP3
players from 2006 through 2012.
The function f(x) = - 0.9x2+ 16x + 10 models the percentage of students that owned portable MP3
players at State University , f(x), x years after 2006.
a. Use the function to find the percentage of of students that owned portable MP3 players at State
University in 2011. Does this overestimate or underestimate the percentage in the graph? By how
much?
b. Use the function to determine the first year in which 80% of students owned portable MP3
players at State University.
132)
A)
a. 67.5%; overestimates by 1.5%
b. 2014
B)
a. 67.5%; underestimates by 1.5%
b. 2014
C)
a. 67.5%; underestimates by 1.5%
b. 2015
D)
a. 67.5%; overestimates by 1.5%
b. 2015
Solve the equation by the method of your choice. Simplify solutions, if possible.
133)
7x2- 41x - 6 = 0
133)
A)
-1
7, 7
B)
{-7, 6}
C)
-1
7, 6
D)
1
41 , -1
7
Solve.
134)
The function s(t) = 16t2 models the distance, s(t), in feet, that an object falls in t seconds. Find the
number of seconds a sky diver is in free fall after jumping from a plane if she falls 368 feet before
opening a parachute. Express your answer in simplified radical form.
134)
A)
16 23 sec
B)
92 sec
C)
23 sec
D)
23 sec
Write a quadratic equation in standard form with the given solution set.
135)
5
4, 3
8
135)
A)
32x2-15x +52 = 0
B)
32x2+15x +52 = 0
C)
32x2-52x +15 = 0
D)
32x2+52x +15 = 0
Complete the square for the binomial. Then factor the resulting perfect square trinomial.
136)
x2+4
9x
136)
A)
8
81 ; x2+4
9x +8
81 =x +4
9
2
B)
4
9; x2+4
9x +4
9=x +2
9
2
C)
2
81 ; x2+4
9x +2
81 =x +2
9
2
D)
4
81 ; x2+4
9x +4
81 =x +2
9
2
Find the axis of symmetry of the parabola defined by the given quadratic function.
137)
f(x) =x2- 12x + 7
137)
A)
x = - 29
B)
x = - 6
C)
x = - 12
D)
x =6
48
Use the discriminant to determine the number and type of solutions for the given equation.
138)
9- 7x2= - 7x + 10
138)
A)
two imaginary solutions
B)
two real rational 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.
139)
f(x) = 11(x -4)2+ 7
139)
A)
(11, 4)
B)
(-4, 7)
C)
(7, -4)
D)
(4, 7)
Find the intercepts of the quadratic function.
140)
f(x) =x2-1
140)
A)
x-intercepts: (-1, 0) and (1, 0)
y-intercept: (0, -1)
B)
x-intercept: (-1, 0)
y-intercept: (0, 1)
C)
x-intercepts: none
y-intercept: (0, -1)
D)
x-intercepts: (-1, 0) and (1, 0)
y-intercept: (0, 1)
Solve the problem.
141)
The cost in millions of dollars for a company to manufacture x thousand automobiles is given by
the function C(x) =3x2- 18x +72. Find the number of automobiles that must be produced to
minimize the cost.
141)
A)
3 thousand automobiles
B)
45 thousand automobiles
C)
6 thousand automobiles
D)
9 thousand automobiles
142)
Let f(x) =x2/3 + 3x1/3. Find all x such that f(x) =4.
142)
A)
-1, 4
B)
-4, 1
C)
-64, 1
D)
-1, 64
49
Solve the polynomial inequality and graph the solution set on a number line.
143)
x2+ 11x + 30 > 0
143)
A)
(-5, )
B)
(-, -6) (-5, )
C)
(-, -6)
D)
(-6, -5)
Solve by completing the square.
144)
x2-8x -15 = 0
144)
A)
{4 ±31}
B)
{4 ±15}
C)
{8 ±79}
D)
{-4±31}
Solve the polynomial inequality and graph the solution set on a number line.
145)
x2- 2x 8
145)
A)
[4, )
B)
(-, -2]
C)
[-2, 4]
D)
(-, -2] [4, )
Solve the inequality and graph the solution set on a number line.
146)
x + 11
x + 4 <3
146)
A)
-, -1
2 (4, )
B)
(-, -4) -1
2,
C)
-4, -1
2
D)
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.
147)
f(x) = - 4x2- 4x
147)
A)
Maximum is 1 at x = - 1
2.
B)
Minimum is 1 at x = - 1
2.
C)
Maximum is - 1 at x =1
2.
D)
Minimum is - 1 at x =1
2.
Solve the problem.
148)
The area of a rectangular wall in a classroom is 168 square feet. Its length is 3 feet shorter than three
times its width. Find the length and width of the wall of the classroom.
148)
A)
width =8 ft; length =17 ft
B)
width =8 ft; length =21 ft
C)
width =8 ft; length =27 ft
D)
width =8 ft; length =11 ft
Find the range of the quadratic function.
149)
f(x) = 11(x -4)2+ 7
149)
A)
( , 7]
B)
[7, )
C)
[4, )
D)
[-7, )
Complete the square for the binomial. Then factor the resulting perfect square trinomial.
150)
x2+ 16x
150)
A)
64; x2+ 16x +64 = (x +8)2
B)
16; x2+ 16x +16 = (x +256)2
C)
256; x2+ 16x +256 = (x +16)2
D)
8; x2+ 16x +8= (x +64)2
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
151)
f(x) = - x2+ 2x + 6
151)
A)
(-1, 3)
B)
(1, 7)
C)
(-1, 5)
D)
(2, 6)
Solve the equation by making an appropriate substitution.
152)
x4-20x2+64 = 0
152)
A)
{-2, 2, -4, 4}
B)
{2, 4}
C)
{4, 16}
D)
{-2i, 2i, -4i, 4i}
53
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
153)
7x2-5= 0
153)
A)
±7
5
B)
±7
35
C)
±35
7
D)
±5
7
Solve the problem.
154)
If f(x) = (x - 2)2 , find all values of x for which f(x) =25.
154)
A)
5, -5
B)
-3, 7
C)
-7, -3
D)
27
Solve the quadratic equation by completing the square.
155)
x2+ 12x - 13 = 0
155)
A)
{0, -13}
B)
{-13, 13}
C)
{1, -13}
D)
{-1, 13}
Use the quadratic formula to solve the equation.
156)
x(x - 2) =9
156)
A)
{1 ±10}
B)
{-1±2i 2}
C)
{1 ±2i 2}
D)
{-1±10}
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
54
157)
f(x) =x2-1
157)
A)
vertex: (0, -1)
axis of symmetry: x = 0
B)
vertex: (0, 1)
axis of symmetry: x = 0
C)
vertex: (0, -1)
axis of symmetry: x = 0
D)
vertex: (-1, 0)
axis of symmetry: x = - 1
Solve the equation by the method of your choice. Simplify solutions, if possible.
158)
(x - 1)2+81 = 0
158)
A)
{-8, 10}
B)
{1 ±9i}
C)
{-1±9i}
D)
{-10, 8}
D)
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
159)
5x2=45
159)
A)
{±3 5}
B)
{±5}
C)
{0}
D)
{±3}
Solve the problem.
160)
The hypotenuse of an isosceles right triangle is 10 feet longer than either of its legs. Find the exact
length of each side.
160)
A)
(10 +2) ft, (10 +2) ft, (20 +2) ft
B)
10 ft, 10 ft, 20 ft
C)
10 2 ft, 10 2 ft, (10 +10 2) ft
D)
(10 +10 2) ft, (10 +10 2) ft, (20 +10 2) ft
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
161)
f(x) = (x + 5)2- 5
161)
A)
(-5, -5)
B)
(5, -5)
C)
(-5, 5)
D)
(5, 5)
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
56
162)
y + 4 =(x + 1)2
162)
A)
vertex: (- 1, - 4)
axis of symmetry: x = - 1
B)
vertex: (- 1, - 4)
axis of symmetry: x = - 1
C)
vertex: (- 1, - 4)
axis of symmetry: x = - 1
D)
vertex: (1, - 4)
axis of symmetry: x =1
57
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
163)
x +2
3
2=5
9
163)
A)
5±2
3
B)
-7
3, 1
C)
2±5
3
D)
-2±5
3
Solve the problem.
164)
A ball is thrown upward with an initial velocity of 14 meters per second from a cliff that is
50 meters high. The height of the ball is given by the quadratic equation h = - 4.9t2+14t +100
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 50 meters from the ground. Round your answer to the nearest tenth of a second.
164)
A)
5.0 sec
B)
4.9 sec
C)
6.2 sec
D)
6.3 sec
Solve the rational inequality and graph the solution set on a real number line.
165)
7x +1
12 -3x 0
165)
A)
-, -1
7 (4, )
B)
-1
7, 4
C)
-1
7,
D)
-1
7,4
Solve the polynomial inequality and graph the solution set on a number line.
166)
-3x2+4x 0
166)
A)
-4
3, 0
B)
( , 0] 4
3,
C)
, -4
3 [0, )
D)
0, 4
3
Solve the quadratic equation by completing the square.
167)
x2- 4x + 40 = 0
167)
A)
{8, -4}
B)
{2 ±36i}
C)
{2 +6i}
D)
{2 ±6i}
Solve the equation by making an appropriate substitution.
168)
x -128 - 8 x= 0
168)
A)
{512}
B)
{192}
C)
{256}
D)
{128}
