Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Use the quadratic formula to solve the equation.
234)
9x2+ 5x + 8 = 0
234)
A)
-5
18 ± i 263
18
B)
-5±263
18
C)
5
18 ± i 263
18
D)
5±263
18
Solve the equation by making an appropriate substitution.
235)
(4x - 4)2- 12(4x - 4) + 35 = 0
235)
A)
11
4, 9
4
B)
-3
4, 1
4
C)
3
4, -1
4
D)
-11
4, -9
4
Find the range of the quadratic function.
236)
f(x) =x2+ 4x + 2
236)
A)
[2, )
B)
( , -10]
C)
( , -2]
D)
[-2, )
Use the discriminant to determine the number and type of solutions for the given equation.
237)
x2+ 5x + 8 = 0
237)
A)
two real rational solutions
B)
one (repeated) real rational solution
C)
two real irrational solutions
D)
two imaginary solutions
81
Solve the problem.
238)
April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 29
feet high. The height of the arrow is given by the function h(t) = - 16t2+64t +29, where t is the time
is seconds. What is the maximum height of the arrow?
238)
A)
25 ft
B)
29 ft
C)
64 ft
D)
93 ft
Sketch the graph of the quadratic function. Identify the vertex, intercepts, and the equation for the axis of symmetry.
239)
f(x) =4+5x + x2
239)
A)
vertex: 5
2, -9
4
x-intercepts: (1, 0) and (4, 0)
y-intercept: (0, 4)
axis of symmetry: x =5
2
B)
vertex: -5
2, -9
4
x-intercepts: (-1, 0) and (-4, 0)
y-intercept: (0, 4)
axis of symmetry: x = - 5
2
82
C)
vertex: -5
2, -9
4
x-intercepts: (1, 0) and (4, 0)
y-intercept: (0, 4)
axis of symmetry: x = - 5
2
D)
vertex: 5
2, -9
4
x-intercepts: (-1, 0) and (-4, 0)
y-intercept: (0, 4)
axis of symmetry: x =5
2
Solve the polynomial inequality and graph the solution set on a number line.
240)
x2- 5x - 14 0
240)
A)
[-2, 7]
B)
(-, -2]
[7, )
C)
[7, )
D)
(-, -2]
Solve the problem.
241)
The daily profit in dollars of a specialty cake shop is described by the function
P(x) = - 3x2+168x -1920, 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?
241)
A)
784 cakes
B)
2352 cakes
C)
56 cakes
D)
28 cakes
242)
Let f(x) = 5(6z - 1)-1 and g(x) = 2(6z - 1)-2. Find all x such that f(x) + g(x) = - 2.
242)
A)
-1
6, 0
B)
-1
6, -1
12
C)
-1
6, 1
12
D)
-2, -1
2
Solve the equation by making an appropriate substitution.
243)
2x - 19 x-10 = 0
243)
A)
{100}
B)
1
4, 100
C)
{10}
D)
1
2, 10
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a +
bi.
244)
(x -5)2= - 49
244)
A)
{-5±7i}
B)
{5 ±7i}
C)
{7 ±5i}
D)
±7i
5
Solve the quadratic equation by completing the square.
245)
x2-12x =5
245)
A)
{6 ±41}
B)
{12 ±149 }
C)
{6 ±5}
D)
{-6±41}
Find the axis of symmetry of the parabola defined by the given quadratic function.
246)
y +4=(x + 2)2
246)
A)
y =4
B)
y = - 4
C)
x = - 2
D)
x =2
Find the range of the quadratic function.
247)
f(x) =8- (x + 2)2
247)
A)
[8, )
B)
( , 8]
C)
[-2, )
D)
( , 2]
Solve the problem.
248)
The owner of a video store has determined that the profits P of the store are approximately given
by P(x) = - x2+60x +67, where x is the number of videos rented daily. Find the maximum profit to
the nearest dollar.
248)
A)
$967
B)
$1800
C)
$900
D)
$1867
Write a quadratic equation in standard form with the given solution set.
249)
{-4i, 4i}
249)
A)
x2-8x -16 = 0
B)
x2+8x +16 = 0
C)
x2+16 = 0
D)
x2-16 = 0
Find the intercepts of the quadratic function.
250)
f(x) =(x + 1)2-1
250)
A)
x-intercepts: (0, 0) and (-2, 0)
y-intercept: (0, 0)
B)
x-intercepts: (0, 0) and (-2, 0)
y-intercept: (0, -1)
C)
x-intercepts: (0, 0)
y-intercept: (0, 0)
D)
x-intercepts: (0, 0) and (2, 0)
y-intercept: (0, 0)
Solve the problem.
251)
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the
developer has 300 feet of fencing and does not fence the side along the street, what is the largest
area that can be enclosed?
251)
A)
5625 sq ft
B)
11,250 sq ft
C)
16,875 sq ft
D)
22,500 sq ft
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
252)
f(x) = (x + 4)2+ 6
252)
A)
(6, -4)
B)
(6, -16)
C)
(-4, 6)
D)
(-6, 4)
Solve the equation by the method of your choice. Simplify solutions, if possible.
253)
x2+6x =19
253)
A)
{±2 7}
B)
{2 7±3}
C)
{-3± 2 7}
D)
{-3± 2 14}
Solve the problem.
254)
The length of a rectangular storage room is 8 feet longer than its width. If the area of the room is 84
square feet, find its dimensions.
254)
A)
5 ft by 15 ft
B)
6 ft by 14 ft
C)
5 ft by 13 ft
D)
7 ft by 15 ft
Use the given functions to find all values of x that satisfy the required inequality.
255)
f(x) =6
x -1, g(x) = 1; f(x) < g(x)
255)
A)
(-, 1]
[7, )
B)
(-, 1)
C)
(1, 7)
D)
(-, 1)
(7, )
Use the discriminant to determine the number and type of solutions for the given equation.
256)
25x2+ 10x + 1 = 0
256)
A)
one (repeated) real irrational solution
B)
two real rational 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.
257)
-x -4
x +9
0
257)
A)
[-4, )
B)
(-, -9]
[-4, )
C)
(-9, -4]
D)
(-, -9)
[-4, )
Solve the polynomial inequality and graph the solution set on a number line.
258)
(x + 4)(x - 7) < 0
258)
A)
(-4, 7)
B)
(7, )
C)
(-, -4)
D)
(-, -4)
(7, )
D)
259)
x2+9x
0
259)
A)
(-, -9]
[0, )
B)
[0, )
C)
[-9, 0]
D)
(-, -9]
88
Solve the problem.
260)
The manufacturer of a DVD player has found that the revenue R (in dollars) is R(p) = - 4p2+1110p,
when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is
the maximum revenue to the nearest whole dollar?
260)
A)
$308,025
B)
$77,006
C)
$154,013
D)
$616,050
Use the discriminant to determine the number and type of solutions for the given equation.
261)
x2- 10x + 25 = 0
261)
A)
one (repeated) real rational solution
B)
one (repeated) real irrational solution
C)
two real rational solutions
D)
two real irrational solutions
Write a quadratic equation in standard form with the given solution set.
262)
{2 +7, 2-7}
262)
A)
x2- 3 = 0
B)
x2+4x + 3 = 0
C)
x2+ 3 = 0
D)
x2-4x - 3 = 0
Solve.
263)
A square flower bed is to be enlarged by adding 3 meters on each side. If the larger square has an
area of 169 square meters, what is the length of a side of the original square?
263)
A)
10 m
B)
7 m
C)
16 m
D)
19 m
Solve the equation by making an appropriate substitution.
264)
x4-10x2+24 = 0
264)
A)
{-2, 2, -i 6, i 6}
B)
{2, 6}
C)
{-2, 2, -6, 6}
D)
{4, 6}
89
265)
x2/5 -x1/5 -12 = 0
265)
A)
{-4, 3}
B)
{-1024, 243}
C)
{4, -3}
D)
{1024, -243}
Solve the problem.
266)
The quadratic function f(x) =0.0041x2-0.46x +36.78 models the median, or average, age, y, at
which U.S. men were first married x years after 1900. In which year was this average age at a
minimum? (Round to the nearest year.) What was the average age at first marriage for that year?
(Round to the nearest tenth.)
266)
A)
1954, 36 years old
B)
1956, 49.7 years old
C)
1936, 49.7 years old
D)
1956, 23.9 years old
Sketch the graph of the quadratic function. Identify the vertex, intercepts, and the equation for the axis of symmetry.
267)
f(x) =x2- 5x + 1
267)
90
A)
vertex: 5
2, -51
4
x-intercepts: 5 ±21
2, 0
y-intercept: (0, 1)
axis of symmetry: x =5
2
B)
vertex: (0, 1)
x-intercepts: none
y-intercept: (0, 1)
axis of symmetry: x = 0
C)
vertex: (2, -9)
x-intercepts: (-1, 0) and (5, 0)
y-intercept: (0, -5)
axis of symmetry: x = 2
D)
vertex: -5
2, -51
4
x-intercepts: -5 ±21
2, 0
y-intercept: (0, 1)
axis of symmetry: x = - 5
2
91
Solve the problem.
268)
Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn
with a push mower. If they can cut the lawn in 6 hours working together find how long to the
nearest tenth of an hour it takes for William to cut the lawn alone.
268)
A)
15.1 hr
B)
10.0 hr
C)
10.1 hr
D)
15.0 hr
Find the intercepts of the quadratic function.
269)
f(x) =2+3x + x2
269)
A)
x-intercepts: (-1, 0) and (-2, 0)
y-intercept: (0, -2)
B)
x-intercepts: (1, 0) and (2, 0)
y-intercept: (0, 2)
C)
x-intercepts: (-1, 0) and (-2, 0)
y-intercept: (0, 2)
D)
x-intercepts: (1, 0) and (2, 0)
y-intercept: (0, -2)
Find the range of the quadratic function.
270)
f(x) = (x + 4)2+ 7
270)
A)
[7, )
B)
[4, )
C)
[-7, )
D)
-4, )
Complete the square for the binomial. Then factor the resulting perfect square trinomial.
271)
x2-2
13 x
271)
A)
2
169; x2-2
13 x +2
169 =x -1
13
2
B)
1
169; x2-2
13 x +1
169 =x -1
13
2
C)
1
169; x2-2
13 x +1
169 =x +1
13
2
D)
4
169; x2-2
13 x +4
169 =x -2
13
2
