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Solve the polynomial inequality and graph the solution set on a number line.
169)
x3+ 4x2+ 8x + 15
0
169)
A)
( , -3]
[5, )
B)
[-3, )
C)
( , -3]
[1, 5]
D)
( , -3]
Use the discriminant to determine the number and type of solutions for the given equation.
170)
x2+ 7x - 5 = 0
170)
A)
one (repeated) real rational solution
B)
two imaginary solutions
C)
two real rational solutions
D)
two real irrational solutions
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
171)
f(x) =9- (x + 3)2
171)
A)
(3, 9)
B)
(9, 3)
C)
(-3, 9)
D)
(9, -3)
61
Solve.
172)
Three times the square of the difference between a number and 5 is -12. Find the number(s).
172)
A)
-5 +2i and -5 -2i
B)
5i +2 and 5i -2
C)
5 +2i 3 and 5 -2i 3
D)
5 +2i and 5 -2i
Complete the square for the binomial. Then factor the resulting perfect square trinomial.
173)
x2+1
4x
173)
A)
1
16 ; x2+1
4x +1
16 =x +1
4
2
B)
1
8; x2+1
4x +1
8=x +1
4
2
C)
64; x2+1
4x +64 =(x +8)2
D)
1
64 ; x2+1
4x +1
64 =x +1
8
2
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
174)
(x + 5)2=28
174)
A)
{2 7±5}
B)
{-5± 2 14}
C)
{-5± 2 7}
D)
{±2 7}
175)
x -5
2
2=49
4
175)
A)
{-1, 6}
B)
{-12, 2}
C)
{-6, 1}
D)
{-2, 12}
Solve the problem.
176)
A person standing close to the edge on top of a 288-foot building throws a baseball vertically
upward. The quadratic function s(t) = - 16t2+ 64t +288 models the ball's height above the ground,
s(t), in feet, t seconds after it was thrown. After how many seconds does the ball reach its maximum
height? Round to the nearest tenth of a second if necessary.
176)
A)
2 sec
B)
6.7 sec
C)
1.5 sec
D)
352 sec
177)
If h(x) =x -5
2
2, find all values of x for which h(x) =25
4.
177)
A)
-5, 0
B)
0, 5
C)
0, 10
D)
-10, 0
Solve.
178)
A ladder that is 17 feet long is 8 feet from the base of a wall. How far up the wall does the ladder
reach?
178)
A)
3 ft
B)
225 ft
C)
353 ft
D)
15 ft
Solve the polynomial inequality and graph the solution set on a number line.
179)
x3- 5x2+ 2x + 8 0
179)
A)
( , -1]
[2, 4]
B)
[-1, 2] [4, )
C)
[-4, -2] [1, )
D)
( , -1]
[4, )
Solve the equation by the method of your choice. Simplify solutions, if possible.
180)
(2x + 5)2=6
180)
A)
-5
2± i 6
2
B)
-5±6
2
C)
-11
2, 1
2
D)
5±6
2
Solve.
181)
The daily number of requests, f(x), for a song that a local radio station receives can be modeled by
the formula f(x) =x2- 5x +8, where x is the number of days after the song has been released.
During which time period will the daily number of requests be below 4?
181)
A)
between day 1 and day 3
B)
between day 1 and day 4
C)
between day 2 and day 6
D)
between day 3 and day 4
Solve the equation by the method of your choice. Simplify solutions, if possible.
182)
8x2- 3x + 1 = 0
182)
A)
3
8± i 23
8
B)
-3
16 ± i 23
16
C)
3
16 ± i 23
16
D)
-3
8± i 23
8
Solve the polynomial inequality and graph the solution set on a number line.
183)
x2+ 6x +9> 0
183)
A)
(-, -3)
B)
(-, -3)
(-3, )
C)
(-3, )
D)
(-, )
65
Solve the rational inequality and graph the solution set on a real number line.
184)
x - 5
x + 7 < 0
184)
A)
(-, -7)
B)
(-, -7)
(5, )
C)
(-7, 5)
D)
(5, )
Solve the equation by the method of your choice. Simplify solutions, if possible.
185)
x2
18 + x +35
9= 0
185)
A)
{-9±11}
B)
{9 ±70}
C)
{9 +11}
D)
{-18 +70}
Use the quadratic formula to solve the equation.
186)
2x2- 7x - 9 = 0
186)
A)
2
9, 0
B)
9
2, -1
C)
2
9, -1
D)
2
9, 1
Find the axis of symmetry of the parabola defined by the given quadratic function.
187)
f(x) = (x + 5)2+ 4
187)
A)
y =4
B)
x = - 5
C)
y = - 4
D)
x =5
Solve the equation by making an appropriate substitution.
188)
(x2-4x)2-17(x2-4x) +60 = 0
188)
A)
{- 2, - 1, 12, 5, 6, 5}
B)
{- 2, - 1, 6, 5}
C)
{12, 5}
D)
{6, 5}
Find the axis of symmetry of the parabola defined by the given quadratic function.
189)
f(x) = (x + 4)2- 3
189)
A)
x =3
B)
x =4
C)
x = - 3
D)
x = - 4
Solve the equation by making an appropriate substitution.
190)
x2/3 - 8x1/3 + 15 = 0
190)
A)
{-125, -27}
B)
{-5, -3}
C)
{27, 125}
D)
{3, 5}
Solve the problem.
191)
A person standing close to the edge on top of a 160-foot building throws a baseball vertically
upward. The quadratic function s(t) = - 16t2+ 64t +160 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 ball finally hits
the ground? Round to the nearest tenth of a second if necessary.
191)
A)
2 sec
B)
1.7 sec
C)
5.7 sec
D)
224 sec
Solve the equation by the method of your choice. Simplify solutions, if possible.
192)
x2+ 18x + 70 = 0
192)
A)
{9 ±70}
B)
{-18 ±70}
C)
{9 ±11}
D)
{-9±11}
Use the discriminant to determine the number and type of solutions for the given equation.
193)
16x2+ 8x = 0
193)
A)
two real irrational solutions
B)
two real rational solutions
C)
one (repeated) real rational solution
D)
two imaginary solutions
Find the axis of symmetry of the parabola defined by the given quadratic function.
194)
f(x) = x2+ 3
194)
A)
x = 0
B)
y =3
C)
x = - 3
D)
x =3
Solve.
195)
Dale inherited $30,000 and invested it in a mutual fund for two years. At the end of the two years,
her investment had grown to $47,628. Determine the annual compound interest rate that would
yield this amount of money. Use the compound interest formula A = P(1 + r)t.
195)
A)
260%
B)
2.6%
C)
26%
D)
0.26%
Solve the equation by the method of your choice. Simplify solutions, if possible.
196)
x2- 3x = 10
196)
A)
-1, 10, -3 ±31
2
B)
2, -5, 3
2±i31
2
C)
-2, 5, 3 ±31
2
D)
-2, 5, 3
2±i31
2
Solve the problem.
197)
If f(x) =(x -7)2, find all values of x for which f(x) = - 4.
197)
A)
7i ±2
B)
±2i
7
C)
7±2i
D)
-7±2i
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.
198)
f(x) =5x2- 15x
198)
A)
Minimum is -45
4 at x = - 3
2.
B)
Maximum is -45
4 at x = - 3
2.
C)
Maximum is -45
4 at x =3
2.
D)
Minimum is -45
4 at x =3
2.
Solve the equation by making an appropriate substitution.
199)
(2x - 4)2=14(2x - 4) - 48
199)
A)
- 5, - 6
B)
1, 2
C)
{6,8}
D)
5, 6
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
200)
x2-2
13 x
200)
A)
1
169; x2-2
13 x +1
169 =x -1
13
2
B)
1
169; x2-2
13 x +1
169 =x +1
13
2
C)
2
169; x2-2
13 x +2
169 =x -1
13
2
D)
4
169; x2-2
13 x +4
169 =x -2
13
2
Find the axis of symmetry of the parabola defined by the given quadratic function.
201)
f(x) = - x2- 8x + 8
201)
A)
x =4
B)
x = - 4
C)
x =24
D)
x = - 8
202)
f(x) =7- (x + 5)2
202)
A)
x = - 5
B)
x = - 7
C)
x =5
D)
x =7
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
203)
25x2+64 = 0
203)
A)
±8
25 i
B)
±8
25
C)
±8
5i
D)
±8
5
Without solving the given quadratic equation, determine the number and type of solutions.
204)
2x2= - 2x - 2
204)
A)
two imaginary solutions
B)
two real irrational solutions
C)
two real rational solutions
D)
one (repeated) real rational solution
Solve the equation by making an appropriate substitution.
205)
x -8 x +15 = 0
205)
A)
{-5, 5, -3, 3}
B)
{25, 9}
C)
{5, 3}
D)
{-5, 5, -3, 3}
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
70
206)
f(x) = (x + 5)2+ 2
206)
A)
vertex (-5, 2); axis of symmetry x = - 5
B)
vertex (-2, 5 ); axis of symmetry x = - 2
C)
vertex (2, -5); axis of symmetry x =2
D)
vertex (5, 2); axis of symmetry x =5
71
Solve the equation by making an appropriate substitution.
207)
(x - 4)2+ 2(x - 4) - 8 = 0
207)
A)
{-8, -2}
B)
{2, 8}
C)
{0, 6}
D)
{-6, 0}
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
208)
f(x) =x2+4
208)
A)
vertex: (0, 4)
axis of symmetry: x = 0
B)
vertex: (0, 4)
axis of symmetry: x = 0
C)
vertex: (4, 0)
axis of symmetry: x =4
D)
vertex: (0,-4)
axis of symmetry: x = 0
72
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
209)
y +4=(x + 2)2
209)
A)
(4, - 2)
B)
(2, - 4)
C)
(4, 2)
D)
(- 2, - 4)
Solve the inequality and graph the solution set on a number line.
210)
x2- 3x - 28 0
210)
A)
(-, -4] [7, )
B)
[-4, 7]
C)
(-, -4]
D)
[7, )
Solve the polynomial inequality and graph the solution set on a number line.
211)
(x + 6)(x - 2)(x - 7) > 0
211)
A)
( , 2)
B)
( , -6)
(2, 7)
C)
(-6, 2) (7, )
D)
(7, )
Solve the quadratic equation by completing the square.
212)
x2+ 12x + 23 = 0
212)
A)
{-12 +23}
B)
{6 ±23}
C)
{-6±13}
D)
{6 +13}
Use the quadratic formula to solve the equation.
213)
2x2+ 12x + 3 = 0
213)
A)
-12 ±30
2
B)
-6±30
2
C)
-6±42
2
D)
-6±30
4
74
Solve the equation by making an appropriate substitution.
214)
2x1/2 - 17x1/4 - 9 = 0
214)
A)
6561, 1
16
B)
{-9, -1}
C)
9, -1
2
D)
{6561}
Solve the rational inequality and graph the solution set on a real number line.
215)
x
x +1 2
215)
A)
[-2, -1)
B)
(-, -2]
(-1, )
C)
(-1, 2]
D)
(-, -1)
[0, )
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
216)
f(x) =x2- 2x -3
216)
75
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
Solve the problem.
217)
A person standing close to the edge on top of a 256-foot building throws a baseball vertically
upward. The quadratic function s(t) = - 16t2+ 64t +256 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 ball finally hits
the ground? Round to the nearest tenth of a second if necessary.
217)
A)
320 sec
B)
2.5 sec
C)
6.5 sec
D)
2 sec
Find the axis of symmetry of the parabola defined by the given quadratic function.
218)
f(x) = 11(x -3)2+ 7
218)
A)
x =3
B)
x = - 3
C)
x =7
D)
x = 11
D)
Solve the equation by the method of your choice. Simplify solutions, if possible.
219)
1
x +11 +1
x=1
14
219)
A)
-17 ±905
2
B)
-39 ±905
2
C)
39 ±905
2
D)
17 ±905
2
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
220)
121x2=9
220)
A)
3
11
B)
±3
121
C)
3
121
D)
±3
11
Solve the polynomial inequality and graph the solution set on a number line.
221)
(x + 7)(x - 3)(x - 6) < 0
221)
A)
(6, )
B)
( , 3)
C)
(-7, 3) (6, )
D)
( , -7)
(3, 6)
Solve the problem.
222)
A rain gutter is made from sheets of aluminum that are 27 inches wide. The edges are turned up to
form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 55
square inches. There are two solutions to this problem. Round to the nearest tenth of an inch.
222)
A)
3.0 in. and 13.2 in.
B)
2.2 in. and 24.8 in.
C)
1.8 in. and 19.8 in.
D)
2.5 in. and 11.0 in.
Write a quadratic equation in standard form with the given solution set.
223)
{-8, -1}
223)
A)
x2+9x +8= 0
B)
x2- 9x +8= 0
C)
x2-8x - 9 = 0
D)
x2+8x - 9 = 0
Solve the equation by making an appropriate substitution.
224)
x1/2 -10x1/4 = - 16
224)
A)
{8, 2}
B)
{64, 4}
C)
{-8, -2}
D)
{4096, 16}
Solve the quadratic equation by completing the square.
225)
16x2-5x + 1 = 0
225)
A)
5±39
32
B)
-5±39
32
C)
5
32 ± i 39
32
D)
-5
32 ± i 39
32
Solve.
226)
If a $2000 investment compounded to $2464.20 after 2 years, determine the annual interest rate of
the investment. Use the compound interest formula A = P(1 + r)t.
226)
A)
11%
B)
110%
C)
1.1%
D)
1100%
Find the range of the quadratic function.
227)
f(x) = - 7(x -3)2-7
227)
A)
[-3, )
B)
( , -7]
C)
( , 3]
D)
[-7, )
Solve the equation by the method of your choice. Simplify solutions, if possible.
228)
6x2+ 12x = - 2
228)
A)
-3±6
3
B)
-3±6
12
C)
-3±3
3
D)
-12 ±6
3
79
Solve the equation by making an appropriate substitution.
229)
x -4x1/2 -32 = 0
229)
A)
{128}
B)
{32}
C)
{64}
D)
{48}
Find the axis of symmetry of the parabola defined by the given quadratic function.
230)
f(x) = - 7(x -3)2-4
230)
A)
x =3
B)
x = - 7
C)
x = - 4
D)
x = - 3
Solve the equation by making an appropriate substitution.
231)
(3x - 6)2- 5(3x - 6) - 14 = 0
231)
A)
-13
3, -4
3
B)
1
3, -8
3
C)
13
3, 4
3
D)
-1
6, 8
3
Find the range of the quadratic function.
232)
f(x) = (x + 1)2- 3
232)
A)
[-3, )
B)
( , -3]
C)
[-1, )
D)
( , -1]
Solve the problem.
233)
Among all pairs of numbers whose difference is 34, find a pair whose product is as small as
possible.
233)
A)
51 and 17
B)
-17 and 17
C)
17 and 17
D)
-51 and -17
