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Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Indicate the coordinates of the vertex of the parabola.
1)
y =4x2+ 24x - 1
1)
A)
(-3, 107)
B)
(3, 35)
C)
(-3, -37)
D)
(3, 107)
Solve by completing the square.
2)
4c2+ 7 =-16c
2)
A)
c =- 7
4, c =7
2
B)
c =- 1
2, c =- 7
2
C)
c =- 1
4, c =- 7
4
D)
c =1
2, c =7
2
Solve the problem.
3)
A person standing close to the edge on top of a 80-foot building throws a baseball vertically
upward. The quadratic equation s = -16t2+ 64t +80 models the ball's height above the ground, s, 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.
3)
A)
5.0 seconds
B)
144 seconds
C)
1.5 seconds
D)
2 seconds
Solve.
4)
(2x + 5)2=49
4)
A)
x= ± 27
B)
x=-6, x=1
C)
x=1, x=6
D)
x=0, x = 1
1
Indicate the coordinates of the vertex of the parabola.
5)
y = x2+ 1
5)
A)
(-1, 0)
B)
(1, 0)
C)
(0, 1)
D)
(0, -1)
Solve.
6)
5x2+ 4 =49
6)
A)
x=24.5
B)
x= ± 4
C)
x=3
D)
x= ± 3
Solve the problem.
7)
A ball is thrown vertically upward from the top of a building 96 feet tall with an initial velocity of
80 feet per second. The distance, s (in feet), of the ball from the ground after t seconds is
s =96 +80t - 16t2. After how many seconds does the ball strike the ground?
7)
A)
5
B)
8
C)
6
D)
97
Write the complex number in the form a + bi.
8)
10 +-100
8)
A)
10 - 10i
B)
0
C)
10 + i
D)
10 + 10i
Solve.
9)
The area of a tabletop is 3468 square inches. Determine the length of the table if the width is 0.76
times the length.
9)
A)
66.67 units
B)
48.64 units
C)
68.89 units
D)
67.55 units
Solve by completing the square.
10)
x2+ 3x - 9 = 0
10)
A)
x =-3 - 3 5
2
B)
x =3+ 3 5
2
C)
x = -3±3 5
D)
x =-3 ±3 5
2
Write the complex number in the form a + bi.
11)
5-36 + 6
11)
A)
-30i + 6
B)
35i 2
C)
30i( 2+ 4)
D)
30i + 6
Add or subtract the following complex numbers.
12)
(9 + 6i) - (-5 + i)
12)
A)
14 + 5i
B)
14 - 5i
C)
-14 - 5i
D)
4+ 7i
Use the quadratic formula to solve the equation. If the equation has no real number solution, so state.
13)
2x2+ 8x + 7 = 0
13)
A)
x =-4 ±2
2
B)
x =-8 ±2
2
C)
x =-4 ±2
4
D)
x =-4 ±30
2
Indicate the coordinates of the vertex of the parabola.
14)
y =x2+ 6x + 16
14)
A)
(7, -9)
B)
(-7, 3)
C)
(-3, 7)
D)
(7, -3)
3
Write the imaginary number in terms of i.
15)
--270
15)
A)
3i 30
B)
-3i 30
C)
-330
D)
330
Solve.
16)
(11x -3)2=12
16)
A)
x =3± 2 3
11
B)
x = ± 2 11
C)
x =- 9
11 , x =15
11
D)
x =-3 ± 2 3
11
Write the imaginary number in terms of i.
17)
-1600
17)
A)
±40
B)
-40i
C)
i40
D)
40i
Solve the quadratic equation and write the solutions in terms of i.
18)
x2+9= 0
18)
A)
x =3
B)
x = ± 3i
C)
x =3i
D)
x = ± 3
Indicate the coordinates of the vertex of the parabola.
19)
y =x2+ 2x + 2
19)
A)
(-1, 1)
B)
(-1, -1)
C)
(1, 0)
D)
(0, 1)
4
Using the discriminant, determine the number of x-intercepts the graph of the equation will have. Do not graph the
equation.
20)
y = x2- 8x + 16
20)
A)
two
B)
one
C)
none
Indicate the axis of symmetry of the parabola.
21)
y = -2x2+ 4x + 1
21)
A)
x = -1
B)
x = 1
C)
x = 3
D)
x = 7
Solve by completing the square.
22)
x2=3- 4x
22)
A)
x = -2±7
B)
x = -2±2 7
C)
x = -1±7
D)
x =2+7
Graph the quadratic equation.
23)
y = -4x2- 40x - 101
23)
5
A)
B)
C)
D)
24)
y =x2+ 4x - 5
24)
6
A)
B)
C)
D)
Solve by completing the square.
25)
x2+ 8x =7
25)
A)
x = -4±223
B)
x = -1±23
C)
x = -4±23
D)
x =4+23
Solve the problem.
26)
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the
developer has 220 feet of fencing and does not fence the side along the street, what is the largest
area that can be enclosed?
26)
A)
3025 ft2
B)
6050 ft2
C)
9075 ft2
D)
12,100 ft2
Graph the quadratic equation. Determine the x-intercepts, if they exist. Identify the vertex and axis of symmetry.
27)
y =6+5x + x2
27)
A)
vertex: (5
2, - 1
4)
x-intercepts: (-3, 0) and (-2, 0)
B)
vertex: (- 5
2, - 1
4)
x-intercepts: (3, 0) and (2, 0)
C)
vertex: (- 5
2, - 1
4)
x-intercepts: (-3, 0) and (-2, 0)
D)
vertex: (5
2, - 1
4)
x-intercepts: (3, 0) and (2, 0)
8
Solve.
28)
(2x + 5)2=5
28)
A)
x =-5 ±5
2
B)
x = - 5 , x =0
C)
x =5±5
2
D)
x =5±5
2
Solve the problem.
29)
A person standing close to the edge on top of a 256-foot building throws a baseball vertically
upward. The quadratic equation s = -16t2+ 64t +256 models the ball's height above the ground, s,
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.
29)
A)
6.5 seconds
B)
320 seconds
C)
2.5 seconds
D)
2 seconds
Graph the quadratic equation.
30)
y = -x2- 6x - 5
30)
A)
B)
9
C)
D)
Solve the problem.
31)
A common equation used in business is a demand equation. It expresses the relationship between
the unit price of some commodity and the quantity demanded. In the demand equation
p = -x2+86, for a certain style of calculator, p is the price per calculator in dollars and x is the
quantity demanded in thousands. Find the demand for the calculator if the price is $5 per
calculator.
31)
A)
10 thousand units
B)
61 thousand units
C)
401
2 thousand units
D)
9 thousand units
Add or subtract the following complex numbers.
32)
7i + (-6 - i)
32)
A)
-6+ 8i
B)
6- 8i
C)
6- 6i
D)
-6+ 6i
10
Determine whether the equation has two distinct real number solutions, one real number solution, or no real number
solution.
33)
5x2=2x - 3
33)
A)
no real number solutions
B)
one real number solution
C)
two real number solutions
Add or subtract the following complex numbers.
34)
6i + (-9 - i)
34)
A)
9- 7i
B)
-9+ 5i
C)
9- 5i
D)
-9+ 7i
Solve by completing the square.
35)
5x2- 2x -6= 0
35)
A)
x =-6, x =32
5
B)
x =-1 ±31
5
C)
x =5±31
25
D)
x =1 ±31
5
Solve the problem.
36)
The distance, s, in feet traveled by a freely falling object is given by the formula s = 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 400 feet high.
36)
A)
6 seconds
B)
5 seconds
C)
4 seconds
D)
25 seconds
Solve.
37)
y2=6
37)
A)
y =36
B)
y =3
C)
y =6
D)
y = ± 6
38)
(x - 3)2=25
38)
A)
x=-8, x=-2
B)
x=28
C)
x= ± 5
D)
x=-2, x=8
Indicate the axis of symmetry of the parabola.
39)
y =x2+ 4x + 12
39)
A)
x =8
B)
x =-8
C)
x =4
D)
x =-2
Solve the problem.
40)
The length of a rectangular storage room is 2 feet longer than its width. If the area of the room is 80
square feet, find its dimensions.
40)
A)
w =9 ft; l =11 ft
B)
w =7 ft; l =9 ft
C)
w =8 ft; l =10 ft
D)
w =7 ft; l =11 ft
Solve by completing the square.
41)
3x2+21x =- 36
41)
A)
No real solution
B)
x = - 1
2, x =1
2
C)
x =3, x =4
D)
x =- 4, x =- 3
Graph the quadratic equation. Determine the x-intercepts, if they exist. Identify the vertex and axis of symmetry.
12
42)
y = -x2+ 2x +8
42)
A)
vertex: (1, 9)
x-intercepts: (-4, 0) and (2, 0)
B)
vertex: (1, - 9)
x-intercepts: (-2, 0) and (4, 0)
C)
vertex: (- 1, 9)
x-intercepts: (-4, 0) and (2, 0)
D)
vertex: (1, 9)
x-intercepts: (-2, 0) and (4, 0)
13
Solve by completing the square.
43)
x2+ 8x - 3 = 0
43)
A)
x =4+19
B)
x = -1±19
C)
x = -4±19
D)
x = -4±219
Use the quadratic formula to solve the equation. If the equation has no real number solution, so state.
44)
x2+ 6x - 16 = 0
44)
A)
x =-2, x =8
B)
x = -8, x = 1
C)
x =8, x =2
D)
x = -8, x =2
Graph the quadratic equation.
45)
y =x2- 4x + 3
45)
A)
B)
14
C)
D)
Write the imaginary number in terms of i.
46)
-49
46)
A)
±7
B)
i 7
C)
7i
D)
-7i
Use the quadratic formula to solve the equation. If the equation has no real number solution, so state.
47)
2x2+ x -7= 0
47)
A)
x =-1 ±57
4
B)
No solution
C)
x =-1 ±57
2
D)
x =1 ±57
4
Add or subtract the following complex numbers.
48)
(6 - 9i) + (5+ 5i)
48)
A)
11 - 4i
B)
11 + 4i
C)
-11 + 4i
D)
1+ 14i
15
Solve by completing the square.
49)
x2+ 2x - 35 = 0
49)
A)
x =-5, x =7
B)
x =-7, x =5
C)
x = ± 35
D)
x =-7, x =-28
Solve.
50)
x2=196
50)
A)
x = ± 15
B)
x =98
C)
x =14
D)
x = ± 14
Solve by completing the square.
51)
x2+ 16x + 42 = 0
51)
A)
x =8+22
B)
x = -8±22
C)
x =8±42
D)
x = -16 +42
Indicate the coordinates of the vertex of the parabola.
52)
y = -2x2+ 4x + 1
52)
A)
(-1, -5)
B)
(1, 3)
C)
(1, 7)
D)
(-1, 3)
Solve the problem.
53)
A ladder that is 10 feet long is 6 feet from the base of a wall. How far up the wall does the ladder
reach?
53)
A)
64 ft
B)
8 ft
C)
234 ft
D)
2 ft
Use the quadratic formula to solve the equation. If the equation has no real number solution, so state.
54)
3x2=-8x - 2
54)
A)
x =-4 ±22
3
B)
x =-4 ±10
6
C)
x =-4 ±10
3
D)
x =-8 ±10
3
Solve the problem.
55)
The product of a number and 1 less than the number is 6. Find the number.
55)
A)
-3 or 2
B)
-2 or 3
C)
-4 or 1
D)
-1 or 4
Solve the equation using the quadratic formula.
56)
x2+ 12x + 26 = 0
56)
A)
x = -12 +26
B)
x =6+10
C)
x = -6±10
D)
x =6±26
Provide an appropriate response.
57)
Write a perfect square trinomial that has a term of 8x.
57)
A)
x2+ 8x +16
B)
x2+ 8x +64
C)
x2+ 8x +4
D)
x2+ 8x +8
Solve by completing the square.
58)
x2-12x -5= 0
58)
A)
x =12 ±149
B)
x =6±41
C)
x =6±5
D)
x =-6 ±41
Solve the problem.
59)
A developer wants to enclose a rectangular grassy lot that borders a city street for parking as
shown in the figure. If the developer has 332 feet of fencing and does not fence the side along the
street, what is the largest area that can be enclosed?
x x
332- 2x
59)
A)
6889 ft2
B)
13,778 ft2
C)
20,667 ft2
D)
27,556 ft2
Solve the equation using the quadratic formula.
60)
6x2+ 12x =- 2
60)
A)
x =-3 ±3
3
B)
x =-3 ±6
3
C)
x =-3 ±6
12
D)
x =-12 ±6
3
Determine the x-intercepts of the graph of the quadratic equation.
61)
y =x2- 4x + 7
61)
A)
(4, 0)
B)
(2, 0), (-2, 0)
C)
(-4, 0)
D)
none
Graph the quadratic equation.
18
62)
y =-3x2+ 36x - 111
62)
A)
B)
C)
D)
19
Indicate the axis of symmetry of the parabola.
63)
y =1
4x2- x + 5
63)
A)
x = -2
B)
x = 8
C)
x = 2
D)
x = 4
Graph the quadratic equation. Identify the vertex and axis of symmetry.
64)
y = -x2- 3
64)
A)
vertex (3, 0)
axis of symmetry: x =3
B)
vertex (0,3)
axis of symmetry: x = 0
C)
vertex (-3, 0)
axis of symmetry: x =-3
D)
vertex (0,-3)
axis of symmetry: x = 0
Indicate the axis of symmetry of the parabola.
65)
y =x2+ 4x + 6
65)
A)
x = 0
B)
x =-2
C)
x =2
D)
x =6
Solve.
66)
The product of two positive numbers is 240. Determine the numbers if the larger number is 3.75
times the smaller number.
66)
A)
8 and 30
B)
1 and 240
C)
6 and 31
D)
9 and 29
Using the discriminant, determine the number of x-intercepts the graph of the equation will have. Do not graph the
equation.
67)
y =- 3x2- 8x - 7
67)
A)
two
B)
one
C)
none
Solve.
68)
The length of a vegetable garden is 6 feet longer than its width. If the area of the garden is 55
square feet, find its dimensions.
68)
A)
w =5 ft; l =11 ft
B)
w =4 ft; l =12 ft
C)
w =4 ft; l =10 ft
D)
w =6 ft; l =12 ft
Solve the equation using the quadratic formula.
69)
6x2+ 8x + 1 = 0
69)
A)
x =-4 ±22
6
B)
x =-8 ±10
6
C)
x =-4 ±10
12
D)
x =-4 ±10
6
Add or subtract the following complex numbers.
70)
(9 + 8i) - (-3 + i)
70)
A)
-12 - 7i
B)
12 - 7i
C)
12 + 7i
D)
6+ 9i
Graph the quadratic equation. Identify the vertex and axis of symmetry.
71)
y = x2- 3
71)
A)
vertex (3, 0)
axis of symmetry: x =3
B)
vertex (0, 3)
axis of symmetry: x = 0
22
C)
vertex (-3, 0)
axis of symmetry: x =-3
D)
vertex (0, -3)
axis of symmetry: x = 0
Solve the quadratic equation and write the solutions in terms of i.
72)
x2- 14x + 85 = 0
72)
A)
x =7±36i
B)
x =13, x =1
C)
x =7+6i
D)
x =7±6i
Determine whether the equation has two distinct real number solutions, one real number solution, or no real number
solution.
73)
x2+ 2x + 1 = 0
73)
A)
no real number solution
B)
one real number solution
C)
two real number solutions
Graph the quadratic equation. Determine the x-intercepts, if they exist. Identify the vertex and axis of symmetry.
23
74)
y =x2- 5x + 1
74)
A)
vertex: (-5
2, -51
4)
x-intercepts: (-5 ±21
2, 0)
B)
vertex: (0, 1)
x-intercepts: none
C)
vertex: (2, -9)
x-intercepts: (-1, 0) and (5, 0)
D)
vertex: (5
2, -51
4)
x-intercepts: (5 ±21
2, 0)
24
Solve the problem.
75)
The number of diagonals, d, in a polygon with n sides is given by the formula d =n2- 3n
2. If a
polygon has 44 diagonals, how many sides does it have?
75)
A)
11 sides
B)
14 sides
C)
9 sides
D)
88 sides
Write the imaginary number in terms of i.
76)
-324
76)
A)
18i
B)
±18
C)
-i18
D)
-18i
Solve the quadratic equation and write the solutions in terms of i.
77)
5x2+ 70x + 425 = 0
77)
A)
x =-7 +6i
B)
x =-7 ±36i
C)
x =-7 ±6i
D)
x =-1, x =-13
Solve the equation using the quadratic formula.
78)
6x2=-12x - 4
78)
A)
x =-3 ±3
3
B)
x =-12 ±3
3
C)
x =-3 ±3
12
D)
x =-3 ±15
3
Using the discriminant, determine the number of x-intercepts the graph of the equation will have. Do not graph the
equation.
79)
y = x2- 4x + 3
79)
A)
one
B)
two
C)
none
25
Write the imaginary number in terms of i.
80)
-292
80)
A)
2i 73
B)
-273
C)
-2i 73
D)
273
Graph the quadratic equation.
81)
y = -x2+ 8x - 7
81)
A)
B)
C)
D)
D)
Indicate the axis of symmetry of the parabola.
82)
y =4x2+ 24x - 1
82)
A)
x = 3
B)
x = -3
C)
x = -37
D)
x = 107
Use the quadratic formula to solve the equation. If the equation has no real number solution, so state.
83)
x2+7x +3= 0
83)
A)
x =-7 ±37
14
B)
x =7±37
2
C)
x =-7 ±61
2
D)
x =-7 ±37
2
Solve.
84)
The area of a square is found by the equation A =s2 where s is the length of a side. If the area of a
square porch is 64 square feet, find the dimensions of the porch.
84)
A)
10 ft by 10 ft
B)
8 ft by 8 ft
C)
9 ft by 9 ft
D)
7 ft by 7 ft
Fill in the blank to make a perfect square trinomial.
85)
x2+ 8x
85)
A)
+ 8
B)
+ 4
C)
+ 16
D)
+ 64
Solve the quadratic equation and write the solutions in terms of i.
86)
x2+ x + 9 = 0
86)
A)
x =-1 ±35
2
B)
x =1
2±35
2i
C)
x = - 1
2±35
2i
D)
x =1 ±35
2
27
Solve.
87)
7x2=175
87)
A)
x= ± 7
B)
x= ± 5
C)
x=0
D)
x= ± 5 7
Write the complex number in the form a + bi.
88)
8+-18
88)
A)
8-3i 2
B)
8+3 2i
C)
8+3i -2
D)
8+3i 2
Solve.
89)
4x2=28
89)
A)
x= ± 7
B)
x=8
C)
x=14
D)
x= ± 7
Solve the equation using the quadratic formula.
90)
4x2=52
90)
A)
x = ± 13
B)
x =26
C)
x =14
D)
x = ± 13
Fill in the blank to make a perfect square trinomial.
91)
x2- 4x
91)
A)
- 16
B)
+ 16
C)
+ 4
D)
- 4
Graph the quadratic equation. Determine the x-intercepts, if they exist. Identify the vertex and axis of symmetry.
28
92)
y =x2+ 4x - 7
92)
A)
vertex: (-2, -11)
x-intercepts: (-2 ±11, 0)
B)
vertex: (-2, 3)
x-intercepts: none
C)
vertex: (4, 0)
x-intercept: (4, 0)
D)
vertex: (-1
2, -121
4)
x-intercepts: (-4, 0) and (3, 0)
Write the imaginary number in terms of i.
93)
-192
93)
A)
-8i 3
B)
8 3
C)
-8 3
D)
8i 3
Indicate the coordinates of the vertex of the parabola.
94)
y =1
4x2- x + 5
94)
A)
(2, 8)
B)
(-2, 4)
C)
(-2, 8)
D)
(2, 4)
Solve the quadratic equation and write the solutions in terms of i.
95)
x2- 14x + 74 = 0
95)
A)
x =7±25i
B)
x =7+5i
C)
x =2, x =12
D)
x =7±5i
Solve by completing the square.
96)
a2- 2a - 24 = 0
96)
A)
a = ± -24
B)
a =-6, a =4
C)
a =-20,a =-4
D)
a =6, a =-4
Solve the problem.
97)
A 30-foot pole is supported by two wires that extend from the top of the pole to points that are
each 16 feet from the base of the pole. Find the total length of the two wires.
97)
A)
68 ft
B)
2312 ft
C)
92 ft
D)
34 ft
98)
An area is to be fenced as shown in the figure. Only 308 feet of fencing is available. The fenced-in
area is A = length·width or A = x(154- x) = -x2+154x.
154- x
x x
154- x
i) Graph A = -x2+154x (using your graphing calculator)
ii) Using the graph, estimate the value of x that will yield the maximum area.
iii) Find the maximum area.
98)
A)
ii) x =75 ft
iii) A =5925 ft2
B)
ii) x =154 ft
iii) A =0ft2
C)
ii) x =38.5 ft
iii) A =4446.75 ft2
D)
ii) x =77 ft
iii) A =5929 ft2
Graph the quadratic equation. Identify the vertex and axis of symmetry.
99)
y =x2-1
99)
31
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
Provide an appropriate response.
100)
Write a perfect square trinomial that has a term of -18x.
100)
A)
x2- 18x +81
B)
x2- 18x +324
C)
x2- 18x -81
D)
x2- 18x -324
Determine the x-intercepts of the graph of the quadratic equation.
101)
y = -2x2- 12x - 10
101)
A)
(1, 0), (-5, 0)
B)
(-1, 0), (-5, 0)
C)
(-1, 0)
D)
none
Solve the problem.
102)
Scot and Elizabeth recently built a rectangular garden measuring 40 feet by 50 feet. They want to
add a paverstone walkway of uniform width around all sides of the garden. How wide can they
make the walkway if they purchased enough stones to cover 1000 square feet?
102)
A)
5 ft
B)
50 ft
C)
62.5 ft
D)
10 ft
Solve the equation using the quadratic formula.
103)
6x2- 17x - 3 = 0
103)
A)
x = - 1
6, x =1
17
B)
x = - 1
6, x =6
C)
x = - 1
6, x =3
D)
x =-6, x =3
Write the imaginary number in terms of i.
104)
-232
104)
A)
2i 58
B)
-2i 58
C)
258
D)
-258
Solve.
105)
(2x - 3)2=49
105)
A)
x=-5, x=2
B)
x=-4, x=10
C)
x=-2, x=5
D)
x=-10, x=4
Solve the problem.
106)
The formula s = 16t2 models the distance, s, 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 and falling 368 feet before opening a
parachute. Express your answer in simplified radical form.
106)
A)
23 seconds
B)
92 seconds
C)
16 23 seconds
D)
23 seconds
Solve the equation using the quadratic formula.
107)
2x2-6= 0
107)
A)
x =3
B)
x= ± 3
C)
x= ± 6
D)
x= ± 6
2
Determine the x-intercepts of the graph of the quadratic equation.
108)
y =x2+8x +15
108)
A)
(-3, 0), (-5, 0)
B)
(3, 0), (5, 0)
C)
(3, 0), (-5, 0)
D)
none
Determine whether the equation has two distinct real number solutions, one real number solution, or no real number
solution.
109)
x2- 6x + 8 = 0
109)
A)
two real number solutions
B)
one real number solution
C)
no real number solution
Indicate the axis of symmetry of the parabola.
110)
y = x2+ 5
110)
A)
x = 1
B)
x =-5
C)
x =5
D)
x = 0
Graph the quadratic equation. Identify the vertex and axis of symmetry.
34
111)
y =x2+1
111)
A)
vertex: (1, 0)
axis of symmetry: x =1
B)
vertex: (0, 1)
axis of symmetry: x = 0
C)
vertex: (0,-1)
axis of symmetry: x = 0
D)
vertex: (0, 1)
axis of symmetry: x = 0
35
Write the imaginary number in terms of i.
112)
-9
112)
A)
-i 3
B)
±3
C)
-3i
D)
3i
Answer Key
Testname: C10
Answer Key
Testname: C10
Answer Key
Testname: C10
