Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph.
1)
x =2y2– 4
1)
A)
B)
C)
D)
Solve.
2)
x2+y2=12
x =y2
2)
A)
(3, 3), (–4, 2)
B)
(3, –3), (3, 3), (–4, –2), (–4, 2)
C)
(3, 3)
D)
(3, –3), (3, 3)
1
3)
x2+(y + 1)2=36
y =x2+5
3)
A)
(–i 3, –8), (i 3, –8), (–10, 5), ( 10, 5)
B)
(0, 5), (–i13, –8), (i13, –8)
C)
(5, 0), (–8, –i13), (–8, i13)
D)
(–3, 8), ( 3, 8), (–i10, –5), (i10, –5)
4)
15x2–8y2=15
8x2–8y2=8
4)
A)
(–6, –i37), (–6, i37), (6, –35), (6, 35)
B)
(–6, –35), (–6, 35), (6, –35), (6, 35)
C)
(–6, –37), (–6, 37), (6, –37), (6, 37)
D)
(–6, –i35), (–6, i37), (6, –37), (6, 37)
Graph.
5)
y = –4x2– 4
5)
A)
B)
C)
D)
2
6)
y2–9x2=144
6)
A)
B)
C)
D)
Solve.
7)
x2+ y2=113
y = x – 1
7)
A)
(7, –8), (8, –7)
B)
(7, 8), (8, 7)
C)
(–7, –8), (8, 7)
D)
(–7, 8), (–8, 7)
3
Write the equation in standard form. Then identify the vertex of the parabola.
8)
x =y2+ 8y – 2
8)
A)
x =(y – 4)2– 2; (–2, –4)
B)
x =(y + 4)2– 18; (–18, 4)
C)
x =(y + 4)2– 18; (–18, –4)
D)
x =(y + 4)2–16; (–16, –4)
Graph.
9)
9x2+y2=36
9)
A)
B)
C)
D)
4
10)
x = –3(y – 4)2
10)
A)
B)
C)
D)
Solve the nonlinear inequality.
5
11)
25x2–9y2225
11)
A)
B)
C)
D)
6
Graph.
12)
x2+ (y – 4)2=36
12)
A)
B)
C)
D)
Solve the nonlinear system of inequalities.
7
13)
y >x2–5
x2
36 +y2
25 < 1
13)
A)
B)
C)
D)
Identify the vertex and axis of symmetry of the parabola.
14)
y =3
7(x + 7)2– 2
14)
A)
Vertex: (–7, 2);
Axis of symmetry: x = –7
B)
Vertex: (–7, –2);
Axis of symmetry: x = –7
C)
Vertex: (–7, –2);
Axis of symmetry: y = –2
D)
Vertex: (7, –2);
Axis of symmetry: x =7
8
Find the equation of the circle with the given center and radius.
15)
Center: (–9, 5); radius: 3
15)
A)
(x + 9)2+ (y – 5)2=3
B)
(x + 5)2+ (y – 9)2=9
C)
(x – 5)2+ (y + 9)2=9
D)
(x – 9)2+ (y + 5)2=3
Identify the vertex and axis of symmetry of the parabola.
16)
x = –4(y + 5)2
16)
A)
Vertex: (–5, 0);
Axis of symmetry: y = 0
B)
Vertex: (0, –5);
Axis of symmetry: y = –5
C)
Vertex: (0, 5);
Axis of symmetry: y =5
D)
Vertex: (–5, 0);
Axis of symmetry: x = –5
Graph.
17)
x2
4+y2
16 = 1
17)
A)
B)
9
C)
D)
Find the coordinates of the midpoint of the line segment joining the points.
18)
(–5, 5) and (–1, –7)
18)
A)
(–6, –2)
B)
– 2, 6
C)
– 3, – 1
D)
(–4, 12)
Identify the vertex and axis of symmetry of the parabola.
19)
y = –3x2– 5
19)
A)
Vertex: (–5, 0);
Axis of symmetry: y = 0
B)
Vertex: (–5, 0);
Axis of symmetry: x = –5
C)
Vertex: (0, –5);
Axis of symmetry: x = 0
D)
Vertex: (0, 5);
Axis of symmetry: x = 0
Solve the problem.
20)
A power outage affected all homes and businesses within a 15 mi radius of the power station. If the
power station is located 11 mi north of the center of town, find an equation of the circle consisting
of the furthest points from the station affected by the power outage.
20)
A)
x2+(y +11)2=225
B)
x2+(y –11)2=15
C)
x2+y2=225
D)
x2+(y –11)2=225
Solve by graphing.
21)
x2
4–y2
25
1
x2
36 +y2
4
1
21)
10
A)
B)
C)
D)
Find the equation in standard form of a hyperbola centered at the origin that passes through the given points and whose
graph approaches the given asymptotes.
22)
(0, –4) and (0, 4); y = – 2
3x and y =2
3x
22)
A)
y2
36 –x2
16 = 1
B)
y2
4–x2
6= 1
C)
x2
16 –y2
36 = 1
D)
y2
16 –x2
36 = 1
11
Graph.
23)
25x2+49y2=1225
23)
A)
B)
C)
D)
Identify the vertex and axis of symmetry of the parabola.
24)
x = –2y2+ 8y – 7
24)
A)
Vertex (1, 2);
Axis of symmetry y =2
B)
Vertex (–1, –2);
Axis of symmetry y = –2
C)
Vertex (1, –2);
Axis of symmetry y = –2
D)
Vertex (–1, 2);
Axis of symmetry y =2
12
Write the equation in standard form. Then identify the vertex of the parabola.
25)
y =x2+ 10x – 2
25)
A)
y =(x – 5)2– 2; (–5, –2)
B)
y =(x + 5)2– 27; (–5, –27)
C)
y =(x + 5)2– 27; (5, –27)
D)
y =(x + 5)2–25; (–5, –25)
Graph.
26)
y =1
9(x + 4)2+ 6
26)
A)
B)
C)
D)
13
Solve the problem.
27)
A power outage affected all homes and businesses within a 3 mi radius of the power station. If the
power station is located 3 mi west and 3 mi north of the center of town, find an equation of the
circle consisting of the furthest points from the station affected by the power outage.
27)
A)
(x + 3)2+ (y – 3)2=9
B)
(x – 3)2+ (y + 3)2=9
C)
(x – 3)2+ (y – 3)2=9
D)
(x + 3)2+ (y + 3)2=9
Solve the nonlinear inequality.
28)
4y2–9x2>36
28)
A)
B)
C)
D)
14
Find the distance between the two points on the coordinate plane. If necessary, round the answer to the nearest
thousandth.
29)
(–3 3, 710) and (–7 3, 210)
29)
A)
298 units 17.263 units
B)
298 units
C)
62 units
D)
62 units 7.874 units
Find the coordinates of the midpoint of the line segment joining the points.
30)
(–2, 1) and (0, 3)
30)
A)
–2
2, 1 +3
2
B)
–2+3
2, 1
2
C)
2
2, 1 –3
2
D)
(–2, 1 +3)
Graph.
31)
7x2+4y2=56
31)
A)
B)
C)
D)
15
Solve the problem.
32)
A homeowner wants to plant a flower garden and a vegetable garden on two separate square plots
of land. She determines that the length of the vegetable garden is to be at least 1 meter longer than
the length of the flower garden and that the combined area of the two gardens is not to exceed 49
square meters. Write a system to represent the situation, letting x represent the length of the flower
garden and y represent the length of the vegetable garden. Then graph the system.
32)
A)
x2+y249
y x + 1
B)
x2+y249
y x + 1
C)
x2+y249
y x – 1
D)
x2+y249
y x – 1
16
Find the equation in standard form of a hyperbola centered at the origin that passes through the given points and whose
graph approaches the given asymptotes.
33)
(–4, 0) and (4, 0); y = – 3
2x and y =3
2x
33)
A)
x2
36 –y2
16 = 1
B)
x2
16 –y2
36 = 1
C)
x2
4–y2
6= 1
D)
y2
16 –x2
36 = 1
Solve the nonlinear inequality.
34)
16x2+64y21024
34)
A)
B)
C)
D)
17
Find the equation in standard form of the parabola whose graph is shown.
35)
35)
A)
y =4x2+ 1
B)
x =4(y – 1)2
C)
x = –4y2+ 1
D)
x =4y2+ 1
18
Graph.
36)
x2+ y2=64
36)
A)
B)
C)
D)
Solve the problem.
37)
A gardener has 44 feet of fencing to enclose his garden. Find the dimensions that will produce a
garden with maximum area. What is the maximum area?
37)
A)
2.75 sq. ft
B)
11 sq. ft
C)
121 sq. ft
D)
484 sq. ft
19
Find the equation in standard form of the parabola whose graph is shown.
38)
38)
A)
x = – 1
2(y + 1)2+5
B)
y = –2(x – 1)2–5
C)
y = – 1
2(x + 1)2+5
D)
y =1
2(x + 1)2+5
Find the equation in standard form of an ellipse centered at the origin that passes through the given points.
39)
(–4, 0), (4, 0), (0, –9), and (0, 9)
39)
A)
x2
16 +y2
81 = 1
B)
x2
81 +y2
16 = 1
C)
x2
4+y2
9= 1
D)
16x2+81y2= 1
Solve the problem.
40)
A bridge with a semi–elliptical arch extends over a river as shown. Find an equation of the ellipse
that represents the arch of the bridge.
15 ft
14 ft
40)
A)
x2
196 +y2
225 = 1
B)
x2
49 +y2
225 = 1
C)
x2
225 +y2
49 = 1
D)
x2
225 +y2
196 = 1
41)
A radio station emits a signal that can be received within a 30 mile radius of the station’s location.
Another radio station located 70 miles east emits a signal that can be received within a 60 mile
radius of the station’s location. The system of inequalities
x2+y2900
(x –70)2+y23600
can be used to determine the region in which both radio station signals can be received. Graph this
system.
41)
20
A)
B)
C)
D)
Identify the vertex and axis of symmetry of the parabola.
42)
x =5y2+ 5
42)
A)
Vertex: (5, 0);
Axis of symmetry: y = 0
B)
Vertex: (0, 5);
Axis of symmetry: y =5
C)
Vertex: (0, 5);
Axis of symmetry: y = 0
D)
Vertex: (5, 0);
Axis of symmetry: x =5
21
Identify the equation as a parabola, circle, ellipse, or hyperbola.
43)
16y2–16x2=256
43)
A)
Hyperbola
B)
Parabola
C)
Circle
D)
Ellipse
Solve.
44)
x2
3+y2
15 = 1
x2
4+y2
10 = 1
44)
A)
B)
C)
D)
45)
5x2+6y2=24
5x2+5y2=25
45)
A)
(–6, i), ( 6, i)
B)
(–2, –i), (2, –i), (–6, i), ( 6, i)
C)
(–6, –i), (–6, i), ( 6, –i), ( 6, i)
D)
(–6, –i), ( 6, i)
Solve the problem.
46)
A company determines that its cost (in dollars) of producing x machine parts is given by
C =0.2x2+7 and that its revenue (in dollars) for selling x machine parts is given by R =12x – 0.2x2.
Write a system of inequalities that would represent the profit region for producing x machine parts.
Then graph the system.
46)
22
A)
C 0.2x2+7
R 12x – 0.2x2
B)
C 0.2x2+7
R 12x – 0.2x2
C)
C 0.2x2+7
R 12x – 0.2x2
D)
C 0.2x2+7
R 12x – 0.2x2
23
Graph.
47)
36x2+12y2=192
47)
A)
B)
C)
D)
Solve.
48)
x2+ y2=74
x2– y2=24
48)
A)
(–7, –5), (–5, –7)
B)
(7, 5), (5, 7), (–7, –5), (–5, –7)
C)
(7, –5), (7, 5)
D)
(7, 5), (–7, 5), (7, –5), (–7, –5)
Graph.
24
49)
(x – 2)2+ (y – 3)2=36
49)
A)
B)
C)
D)
Use the given information to find the equation of the circle.
50)
Center: (2, 4); passes through the point (5, –1)
50)
A)
(x – 2)2+(y – 4)2=34
B)
(x + 2)2+(y + 4)2=34
C)
(x – 4)2+(y – 2)2=34
D)
(x – 2)2+(y – 4)2=34
Graph.
25
51)
x2
9–y2
4= 1
51)
A)
B)
C)
D)
Find the coordinates of the midpoint of the line segment joining the points.
52)
( 3, –1) and ( 10, –6)
52)
A)
5
2, 3+10
2
B)
3+10
2, 5
2
C)
3+10
2, –7
2
D)
–7
2, 3+10
2
26
Write the equation in standard form. Then identify the vertex of the parabola.
53)
x =y2– 10y +6
53)
A)
x =(y +5)2– 19; (–19, –5)
B)
x =(y –5)2+6; (6, 5)
C)
x =(y –5)2– 19; (–19, 5)
D)
x =(y –5)2+6; (6, –5)
Find the distance between the two points on the coordinate plane. If necessary, round the answer to the nearest
thousandth.
54)
(3, –5) and (7, –7)
54)
A)
2 5 units 4.472 units
B)
6 units
C)
12 units
D)
12 3 units 20.785 units
Solve the problem.
55)
Arches in the shapes of parabolas are often used in construction. Find the equation of a parabolic
arc that is 26 feet high at its highest point and 30 feet wide at the base, as illustrated in the figure.
Place the origin at the midpoint of the base.
26 ft.
30 ft.
55)
A)
y =26
225x2+ 26
B)
y = – 26
225x2+ 26
C)
y = –x2+ 30
D)
y = –x2+ 26
27
Graph.
56)
x2+ y2+ 2x + 8y + 13 = 0
56)
A)
B)
C)
D)
Solve.
57)
4x2–4y2=100
2x2+y2=50
57)
A)
(–5, 0), (5, 0)
B)
(–5, –10), (–5, 10), (5, –10), (5, 10)
C)
(0, –5), (0, 5)
D)
(–5, 10), (5, 10)
Identify the equation as a parabola, circle, ellipse, or hyperbola.
58)
4x2– 9y2=36
58)
A)
Ellipse
B)
Circle
C)
Parabola
D)
Hyperbola
28
Find the center and radius of the the circle.
59)
(x + 2)2+ (y + 5)2=16
59)
A)
Center: (–2, 5);
Radius: 4
B)
Center: (–2, –5);
Radius: 4
C)
Center: (2, –5);
Radius: 4
D)
Center: (2, 5);
Radius: 4
Graph.
60)
16x2+64y2=1024
60)
A)
B)
C)
D)
29
Solve the nonlinear inequality.
61)
16x2–25y2>400
61)
A)
B)
C)
D)
Solve.
62)
x2+ y2=100
x2– y2=100
62)
A)
(10, 0), (10, 10)
B)
(10, 10), (–10, 10)
C)
(–10, 0), (–10, 10)
D)
(10, 0), (–10, 0)
30
Find the coordinates of the midpoint of the line segment joining the points.
63)
5
2, –7
2 and –7
2, 5
2
63)
A)
3, – 3
B)
(144, 144)
C)
(4, 4)
D)
–1
2, –1
2
Write the equation in standard form. Then identify the vertex of the parabola.
64)
x =y2– 9y – 10
64)
A)
x =y +9
22–121
4; –121
4, 9
2
B)
x =y +9
22–121
4; –121
4, –9
2
C)
x =y –9
22– 10; –10, 9
2
D)
x =y –9
22–121
4; –121
4, 9
2
Solve the nonlinear inequality.
65)
y –x2– 3x – 5
65)
A)
B)
31
C)
D)
Find the center and radius of the the circle.
66)
(x – 1)2+ (y + 3)2=9
66)
A)
Center: (–1, –3);
Radius: 3
B)
Center: (1, 3);
Radius: 3
C)
Center: (1, –3);
Radius: 3
D)
Center: (–1, 3);
Radius: 3
Solve.
67)
x2+ y2=61
x + y =11
67)
A)
(–6, 5), (–5, 6)
B)
(6, –5), (5, –6)
C)
(6, 5), (5, 6)
D)
(–6, –5), (–5, –6)
Identify the vertex and axis of symmetry of the parabola.
68)
y =2x2+ 4x + 1
68)
A)
Vertex (–1, –1);
Axis of symmetry x = –1
B)
Vertex (1, –1);
Axis of symmetry x =1
C)
Vertex (–1, 1);
Axis of symmetry x = –1
D)
Vertex (1, 1);
Axis of symmetry x =1
Use the given information to find the equation of the circle.
69)
Center: (0, –1); radius: 3
69)
A)
x2+ (y + 1)2=3
B)
(x + 1)2+ y2=9
C)
x2+ (y – 1)2=3
D)
(x – 1)2+ y2=9
32
Graph.
70)
(x – 4)2+ (y + 2)2=25
70)
A)
B)
C)
D)
Solve by graphing.
33
71)
4x2+y2>64
71)
A)
B)
C)
D)
Write the equation in standard form. Then identify the vertex of the parabola.
72)
y = –2x2+ 7x – 7
72)
A)
y = –2x –7
22+35
2; 7
2, 35
2
B)
y =2x +7
42–105
8; –7
4, –105
8
C)
y = –2x +7
42–7
8; –7
4, –7
8
D)
y = –2x –7
42–7
8; 7
4, –7
8
34
Find the coordinates of the midpoint of the line segment joining the points.
73)
(13 5, –11) and (–5, 0)
73)
A)
7 5, 11
2
B)
610, –33
2
C)
6 5, –11
2
D)
(–5, 11)
Solve the nonlinear system of inequalities.
74)
x2+y236
y –2x + 3
74)
A)
B)
C)
D)
Graph.
35
75)
x2
4+y2
16 = 1
75)
A)
B)
C)
D)
Use the given information to find the equation of the circle.
76)
Center: (–7, 3); radius: 1
76)
A)
(x – 7)2+ (y + 3)2=1
B)
(x + 3)2+ (y – 7)2=1
C)
(x – 3)2+ (y + 7)2=1
D)
(x + 7)2+ (y – 3)2=1
Solve the problem.
77)
If a rock is thrown vertically upward from the top of a building 144 feet high with an initial velocity
of 128 feet per second, the height, h, above ground level after t seconds is given by h = –16t2+128t
+144, where h is in feet and t is in seconds. What is the maximum height the rock will reach?
77)
A)
144 ft
B)
160 ft
C)
400 ft
D)
112 ft
36
Find the center and radius of the the circle.
78)
x2+ y2+ 4x + 12y + 31 = 0
78)
A)
Center: (6, 2);
Radius: 9
B)
Center: (2, 6);
Radius: 9
C)
Center: (–2, –6);
Radius: 3
D)
Center: (–6, –2);
Radius: 3
Write the equation in standard form. Then identify the vertex of the parabola.
79)
x = –2y2+ 5y – 7
79)
A)
x = –2y –5
22+11
2; 11
2, 5
2
B)
x =2y +5
42–81
8; –81
8, –5
4
C)
x = –2y –5
42–31
8; –31
8, 5
4
D)
x = –2y +5
42–31
8; –31
8, –5
4
37
Graph.
80)
x = –y2– 4y – 6
80)
A)
B)
C)
D)
38
81)
25x2– 4y2=100
81)
A)
B)
C)
D)
82)
16x2– 4y2=64
82)
39
A)
B)
C)
D)
40
83)
(x + 1)2+ (y – 4)2=36
83)
A)
B)
C)
D)
Find the distance between the pair of points.
84)
(7, –7) and (6, –4)
84)
A)
8 2 units
B)
8 units
C)
4 units
D)
10 units
Solve the nonlinear inequality.
41
85)
64x2+9y2>576
85)
A)
B)
C)
D)
Solve the problem.
42
86)
In a search and rescue mission, a team maps out an elliptical search region from the last known
location of a pair of hikers. The search region can be represented by the inequality 16x2+49y2
784. Graph this inequality.
86)
A)
B)
C)
D)
Write in standard form the equation of the parabola. Then identify the vertex.
87)
x = –3y2– 18y –84
87)
A)
–3(y + 3)2– 75; (–75, –3)
B)
–3(y + 3)2– 93; ( –3, –93)
C)
–3(y + 3)2– 57; (–57, –3)
D)
–3(y + 3)2– 111; (–111, –3)
Solve the nonlinear system of inequalities.
43
88)
x2
9+y2
25
1
x2
25 +y2
9
1
88)
A)
B)
C)
D)
Use the given information to find the equation of the circle.
89)
Center: (8, 4); passes through the point (11, 8)
89)
A)
(x – 4)2+ (y – 8)2= 9
B)
(x – 8)2+ (y – 4)2= 25
C)
(x + 4)2+ (y + 8)2= 9
D)
(x + 8)2+ (y + 4)2= 25
44
Find the equation in standard form of an ellipse centered at the origin that passes through the given points.
90)
(–7, 0), ( 7, 0), (0, –2 3), and (0, 2 3)
90)
A)
x2
12 +y2
7= 1
B)
x2
7+y2
2 3 = 1
C)
x2
7+y2
12 = 1
D)
7x2+12y2= 1
Solve.
91)
2x2+3y2=3
2x2+2y2=4
91)
A)
(–3, i), ( 3, i)
B)
(–1, –i), (1, –i), (–3, i), ( 3, i)
C)
(–3, –i), ( 3, i)
D)
(–3, –i), (–3, i), ( 3, –i), ( 3, i)
Find the center and radius of the the circle.
92)
(x – 6)2+ (y – 4)2=4
92)
A)
Center: (6, 4);
Radius: 2
B)
Center (–6, 4);
Radius: 2
C)
Center (–6, –4);
Radius: 2
D)
Center (6, –4);
Radius: 2
Use the given information to find the equation of the circle.
93)
Center: (7, 0); radius: 10
93)
A)
x2+ (y – 7)2=100
B)
x2+ (y + 7)2=100
C)
(x + 7)2+ y2=10
D)
(x – 7)2+ y2=10
94)
Center: (4, 0); passes through the point (4, –3)
94)
A)
(x + 4)2+y2=9
B)
x2+(y – 4)2=9
C)
(x – 4)2+y2=9
D)
(x – 4)2+y2=3
Solve the nonlinear system of inequalities.
95)
y 2x2+ 12x + 13
y < –x2– 5
95)
45
A)
B)
C)
No real solutions
D)
96)
x2
9–y2
64
1
x2
49 +y2
9
1
96)
46
A)
B)
C)
D)
Find the midpoint of the line segment joining the pair of points.
97)
(8, –9) and (–9, 0)
97)
A)
(17, –9)
B)
–1
2, –9
2
C)
17
2, –9
2
D)
(–1, –9)
Use the given information to find the equation of the circle.
98)
Center: (5, –7); radius: 11
98)
A)
(x – 5)2+ (y + 7)2=11
B)
(x – 7)2+ (y + 5)2=121
C)
(x + 5)2+ (y – 7)2=11
D)
(x + 7)2+ (y – 5)2=121
Find the distance between the two points on the coordinate plane. If necessary, round the answer to the nearest
thousandth.
99)
(6, –3) and (–5, 5)
99)
A)
19 units
B)
57 units
C)
57 57 units 430.341 units
D)
185 units 13.601 units
Solve the problem.
100)
A lawyer drives from his home, located 10 mi east and 15 mi north of the town courthouse, to his
office, located 3 mi west and 1 mi south of the courthouse. Find the distance between the lawyer’s
home and his office. Round to the nearest mile, if necessary.
100)
A)
19 mi
B)
16 mi
C)
17 mi
D)
21 mi
47
Find the coordinates of the midpoint of the line segment joining the points.
101)
(0, –6) and (9, 5)
101)
A)
–9
2, –11
2
B)
9
2, –1
2
C)
(–9, –11)
D)
(9, –1)
Solve the nonlinear inequality.
102)
(x – 1)2+ (y – 5)2<4
102)
A)
B)
C)
D)
48
Graph.
103)
(x – 2)2+ (y + 1)2=49
103)
A)
B)
C)
D)
49
Solve the problem.
104)
A bridge with a semi–elliptical arch extends over a river as shown. Find an equation of the ellipse
that represents the arch of the bridge.
20 ft
12 ft
104)
A)
x2
400 +y2
144 = 1
B)
x2
400 +y2
36 = 1
C)
x2
144 +y2
400 = 1
D)
x2
36 +y2
400 = 1
Identify the equation as a parabola, circle, ellipse, or hyperbola.
105)
4y2+ x =9
105)
A)
Circle
B)
Ellipse
C)
Parabola
D)
Hyperbola
Find the equation in standard form of a hyperbola centered at the origin that passes through the given points and whose
graph approaches the given asymptotes.
106)
(–3, 0) and (3, 0); y = – 1
3x and y =1
3x
106)
A)
x2
3–y2= 1
B)
y2
9–x2= 1
C)
x2–y2
9= 1
D)
x2
9–y2= 1
Solve the problem.
107)
Two elliptical pathways in a park intersect as shown below. If the equations of the ellipses that
represent the outermost perimeter of the pathways are x2+4y2=2500 and 4x2+y2=2500, at
which points do the pathways intersect?
107)
A)
B)
C)
D)
50
Find the coordinates of the midpoint of the line segment joining the points.
108)
(2, 9) and (4, 3)
108)
A)
3, 6
B)
(–2, 6)
C)
(6, 12)
D)
– 1, 3
Solve the nonlinear system of inequalities.
109)
x2+y236
x2
49 +y2
36
1
109)
A)
B)
C)
D)
No real solutions
Find the center and the radius of the circle.
110)
x2+y2+ 12x – 2y + 34 = 0
110)
A)
(6, –1); 3
B)
(6, –1); 3
C)
(–6, 1); 3
D)
(–6, 1); 3
51
Solve.
111)
y = x2– 8x + 16
y = –x +6
111)
A)
(4, 2)
B)
(5, 11), (2, 4)
C)
(–5, 11), (–2, 8)
D)
(5, 1), (2, 4)
Solve the problem.
112)
A company determines that its cost (in dollars) of producing x machine parts is given by
C =0.3x2+2 and that its revenue (in dollars) for selling x machine parts is given by R =12x – 0.2x2.
Write a system of inequalities that would represent the profit region for producing x machine parts.
Then graph the system.
112)
A)
C 0.3x2+2
R 12x – 0.2x2
B)
C 0.3x2+2
R 12x – 0.2x2
52
C)
C 0.3x2+2
R 12x – 0.2x2
D)
C 0.3x2+2
R 12x – 0.2x2
Graph.
113)
y =3x2– 6x – 2
113)
A)
B)
53
C)
D)
Identify the vertex and axis of symmetry of the parabola.
114)
y = (x + 6)2– 1
114)
A)
Vertex: (–6, –1);
Axis of symmetry: y = –1
B)
Vertex: (–6, –1);
Axis of symmetry: x = –6
C)
Vertex: (–6, 1);
Axis of symmetry: x = –6
D)
Vertex: (6, –1);
Axis of symmetry: x =6
54
Graph.
115)
x = –2y2– 8y – 7
115)
A)
B)
C)
D)
55
Solve the problem.
116)
Arches in the shapes of parabolas are often used in construction. Find the equation of a parabolic
arc that is 18 feet high at its highest point and 26 feet wide at the base, as illustrated in the figure.
Place the origin at the midpoint of the base.
18 ft.
26 ft.
116)
A)
y =18
169x2+ 18
B)
y = – 18
169x2+ 18
C)
y = –x2+ 18
D)
y = –x2+ 26
117)
An elliptical bicycle path is constructed in a local park. The equation of the ellipse that represents
the path, in yards, is given by x2
900 +y2
4900 = 1. What are the length and the width of the bicycle
path?
117)
A)
length: 60 yd; width: 140 yd
B)
length: 140 yd; width: 60 yd
C)
length: 70 yd; width: 30 yd
D)
length: 30 yd; width: 70 yd
56
Graph.
118)
49x2+9y2=441
118)
A)
B)
C)
D)
Use the given information to find the equation of the circle.
119)
Center: (0, –1); radius: 6
119)
A)
x2+ (y + 1)2=36
B)
(x – 1)2+ y2=36
C)
(x + 1)2+ y2=36
D)
x2+ (y – 1)2=6
Solve the nonlinear inequality.
57
120)
x2+16y216
120)
A)
B)
C)
D)
Use the given information to find the equation of the circle.
121)
Center: (–8, 0); radius: 2
121)
A)
(x – 8)2+ y2=4
B)
(x + 8)2+ y2=4
C)
x2+ (y + 8)2=2
D)
x2+ (y – 8)2=2
58
Find the equation in standard form of an ellipse centered at the origin that passes through the given points.
122)
(–9, 0), (9, 0), (0, –5), and (0, 5)
122)
A)
x2
9+y2
5= 1
B)
x2
81 +y2
25 = 1
C)
81x2+25y2= 1
D)
x2
25 +y2
81 = 1
Find the equation in standard form of the parabola whose graph is shown.
123)
123)
A)
y =1
4(x +3)2+9
B)
y =4(x –3)2+9
C)
y =1
4(x –3)2+9
D)
x =1
4(y –3)2+9
Find the distance between the two points on the coordinate plane. If necessary, round the answer to the nearest
thousandth.
124)
(7, 2) and (–4, –1)
124)
A)
130 units 11.402 units
B)
33 units
C)
4 7 units 10.583 units
D)
130 units
59
Graph.
125)
12y2–36x2=192
125)
A)
B)
C)
D)
Find the equation in standard form of a hyperbola centered at the origin that passes through the given points and whose
graph approaches the given asymptotes.
126)
(0, –6) and (0, 6); y = –6x and y =6x
126)
A)
x2
36 –y2= 1
B)
y2–x2
36 = 1
C)
y2
6–x2= 1
D)
y2
36 –x2= 1
Identify the equation as a parabola, circle, ellipse, or hyperbola.
127)
2x2+ 2y2=9
127)
A)
Ellipse
B)
Hyperbola
C)
Parabola
D)
Circle
60
Solve the nonlinear inequality.
128)
(x – 2)2+ (y – 3)29
128)
A)
B)
C)
D)
Graph.
61
129)
9x2–6y2=18
129)
A)
B)
C)
D)
Use the given information to find the equation of the circle.
130)
Endpoints of a diameter: (9, 7) and (–5, 8)
130)
A)
x + 2 2+y –15
22=17
B)
x + 2 2+y +15
22=241
C)
x – 7 2+y +1
22=197
D)
x – 2 2+y –15
22=197
4
62
Solve the problem.
131)
An electronics manufacturer’s revenue R for selling x mobile phones is given by R =0.5x2–90x. A
competing electronics manufacturer’s revenue for selling a similar mobile phone is R =95x. Under
what circumstances will both manufacturers make the same revenue?
131)
A)
B)
C)
D)
Find the center and radius of the the circle.
132)
5x2+ 5y2– 10x + 40y + 40 = 0
132)
A)
Center: (–4, 1);
Radius: 3
B)
Center: (4, –1);
Radius: 9
C)
Center: (1, –4);
Radius: 3
D)
Center: (–1, 4);
Radius: 9
63
Graph.
133)
x =3y2+ 6y – 1
133)
A)
B)
C)
D)
Solve the problem.
134)
If a satellite is placed in a circular orbit of 440 kilometers above the Earth, what is the equation of
the path of the satellite if the origin is placed at the center of the Earth (the diameter of the Earth is
approximately 12,740 kilometers)?
134)
A)
x2+y2=193,600
B)
x2+y2=173,712,400
C)
x2+y2= 40,576,900
D)
x2+y2=46,376,100
64
Solve.
135)
y2
10 –x2
5= 1
y2
19 +x2
19 = 1
135)
A)
(–3, –2), (–3, 2), ( 3, –2), ( 3, 2)
B)
(–i 3, –2), (–i 3, 2), (i 3, –2), (i 3, 2)
C)
(–i 3, –4), (–i 3, 4), (i 3, –4), (i 3, 4)
D)
(–3, –4), (–3, 4), ( 3, –4), ( 3, 4)
Solve the nonlinear system of inequalities.
136)
x2+y216
x2+y236
136)
A)
B)
C)
D)
Solve the nonlinear inequality.
65
137)
4y2–9x236
137)
A)
B)
C)
D)
Find the center and radius of the the circle.
138)
x2+ y2+ 16x + 2y + 65 =9
138)
A)
Center: (–1, –8);
Radius: 3
B)
Center: (–8, –1);
Radius: 3
C)
Center: (1, 8);
Radius: 9
D)
(Center: 8, 1);
Radius: 9
Solve.
139)
x2+y2=49
y =x2–7
139)
A)
(13, 6), (0, 7)
B)
(–13, 6), ( 13, 6), (0, 7)
C)
(13, 6), (0, –7)
D)
(–13, 6), ( 13, 6), (0, –7)
Graph.
66
140)
4x2–y2=64
140)
A)
B)
C)
D)
67
Find the distance between the two points on the coordinate plane. If necessary, round the answer to the nearest
thousandth.
141)
1
2, 1
7 and 3
4, 8
7
141)
A)
17
16 1.031 units
B)
4 units
C)
16
17 0.970 units
D)
1
40.250 units
Solve.
142)
x2+y2=40
x =y2+ 2
142)
A)
(–7, –i 5), (–7, i 5), (6, –2 2), (6, 2 2)
B)
(–7, –3i), (–7, 3i), (6, –2), (6, 2)
C)
(–7, –3), (–7, 3), (6, –2), (6, 2)
D)
(7, –5), (7, 5), (–6, –2i 2), (–6, 2i 2)
Identify the vertex and axis of symmetry of the parabola.
143)
y = –2x2– 4x – 5
143)
A)
Vertex (–1, 3);
Axis of symmetry x = –1
B)
Vertex (–1, –3);
Axis of symmetry x = –1
C)
Vertex (1, 3);
Axis of symmetry x =1
D)
Vertex (1, –3);
Axis of symmetry x =1
Solve the nonlinear system of inequalities.
144)
y – x2– 6x – 4
y x2+ 6x + 4
144)
A)
B)
68
C)
D)
Write the equation in standard form. Then identify the vertex of the parabola.
145)
y =x2– 3x – 8
145)
A)
y =x –3
22– 8; 3
2, –8
B)
y =x –3
22–41
4; 3
2, –41
4
C)
y =x +3
22–41
4; –3
2, –41
4
D)
y =x +3
22–41
4; 3
2, –41
4
Solve the problem.
146)
A wildlife researcher is monitoring a black bear that has a radio telemetry collar with a transmitting
range of 18 miles. The researcher is in a research station with her receiver and tracking the bear’s
movements. If we put the origin of a coordinate system at the research station, what is the equation
of all possible locations of the bear where the transmitter would be at its maximum range?
146)
A)
x2+y2=324
B)
x2+y2=18
C)
x2+y2=36
D)
x2–y2=18
69
Graph.
147)
x2+ y2– 10x – 4y + 25 = 0
147)
A)
B)
C)
D)
Find the distance between the pair of points.
148)
(–1.3, 5.9) and (3.7, –6.1)
148)
A)
17 units
B)
13 units
C)
17 units
D)
169 units
Solve the nonlinear inequality.
70
149)
x2+ y2<4
149)
A)
B)
C)
D)
71
Graph.
150)
(x + 1)2+ (y + 1)2=25
150)
A)
B)
C)
D)
Solve the problem.
72
151)
As a safety precaution, emergency workers evacuated residents within a 6 mile radius of a
chemical spill. The evacuated area can be represented by the inequality x2+ y236. Graph this
inequality.
151)
A)
B)
C)
D)
73
Graph.
152)
x2+ y2=9
152)
A)
B)
C)
D)
Find the coordinates of the midpoint of the line segment joining the points.
153)
(0.1, –7.5) and (4.7, –1.8)
153)
A)
(–2.3, –2.85)
B)
(4.8, –9.3)
C)
(–4.6, –5.7)
D)
(2.4, –4.65)
Solve the nonlinear inequality.
74
154)
y 4x –x2
154)
A)
B)
C)
D)
Solve the problem.
155)
Henry owns a clock repair shop. He has found that the cost of operating his shop is given by
C =2x2– 124x + 68, where C is the cost in dollars, and x is the number of clocks repaired. How
many clocks must he repair to minimize operating costs?
155)
A)
20 clocks
B)
68 clocks
C)
34 clocks
D)
31 clocks
Find the center and radius of the the circle.
156)
(x + 2)2+ (y – 4)2=36
156)
A)
Center: (–2, 4);
Radius: 6
B)
Center: (2, 4);
Radius: 6
C)
Center: (2, –4);
Radius: 6
D)
Center: (–2, –4);
Radius: 6
Solve the nonlinear system of inequalities.
75
157)
x2+y2<9
x2+y2>36
157)
A)
B)
C)
D)
No real solutions
Write the equation in standard form. Then identify the vertex of the parabola.
158)
y = 2x2+ 7x + 6
158)
A)
y =2x +7
22+ 6; –7
4, 6
B)
y =2x +7
42–1
8; –7
4, –1
8
C)
y =2x +7
42–1
8; 7
4, –1
8
D)
y =x +7
22–37
2; –7
2, –37
2
76
159)
y =x2– 6x +5
159)
A)
y =(x –3)2+5; (–3, 5)
B)
y =(x –3)2+5; (3, 5)
C)
y =(x –3)2– 4; (3, –4)
D)
y =(x +3)2– 4; (–3, –4)
Find the distance between the two points on the coordinate plane. If necessary, round the answer to the nearest
thousandth.
160)
(–5.3, 3.9) and (–5.5, –5.6)
160)
A)
113.75 10.665 units
B)
119.53 10.933 units
C)
119.53 units
D)
90.29 9.502 units
Find the coordinates of the midpoint of the line segment joining the points.
161)
(1, –1) and (–6, 1)
161)
A)
–5
2, 0
B)
7
2, – 1
C)
(–5, 0)
D)
(7, –2)
Solve.
162)
6x2–y2=30
y =x2–5
162)
A)
(–11, 6), ( 11, 6)
B)
(–5, 0), ( 5, 0)
C)
(0, –5), (0, 5), (6, –11), (6, 11)
D)
(–5, 0), ( 5, 0), (–11, 6), ( 11, 6)
Solve the nonlinear system of inequalities.
163)
y >x2– 9
y 1
2x – 7
163)
A)
B)
77
C)
D)
Graph.
164)
x2+9y2=81
164)
A)
B)
78
C)
D)
165)
y2
16 –x2
49 = 1
165)
A)
B)
79
C)
D)
Identify the vertex and axis of symmetry of the parabola.
166)
x =3y2– 6y + 7
166)
A)
Vertex (4, 1);
Axis of symmetry y =1
B)
Vertex (–4, –1);
Axis of symmetry y = –1
C)
Vertex (4, –1);
Axis of symmetry y = –1
D)
Vertex (–4, 1);
Axis of symmetry y =1
Solve the problem.
167)
Kara owns a hotdog stand. She has found that her profit is represented by the equation
P = –x2+ 72x + 83, with P being the profit in dollars, and x the number of hotdogs sold. How many
hotdogs must Kara sell to maximize her profit?
167)
A)
36 hotdogs
B)
23 hotdogs
C)
47 hotdogs
D)
37 hotdogs
Solve.
168)
2x2– 2y2= –10
5x2+ 5y2=65
168)
A)
(2, 3), (–2, 3), (2, –3), (–2, –3)
B)
(2, –3), (2, 3)
C)
(2, 3), (3, 2), (–2, –3), (–3, –2)
D)
(–2, –3), (–3, –2)
Graph.
169)
y2
16 –x2
4= 1
169)
80
A)
B)
C)
D)
Identify the vertex and axis of symmetry of the parabola.
170)
x = –y2+ 4y – 2
170)
A)
Vertex (– 6, –2);
Axis of symmetry y = –2
B)
Vertex (6, 2);
Axis of symmetry y =2
C)
Vertex: (2, 2);
Axis of symmetry y =2
D)
Vertex (6, –2);
Axis of symmetry y = –2
Graph.
171)
x =1
2(y + 3)2– 3
171)
81
A)
B)
C)
D)
Solve.
172)
4x2+y2=6
3x2–y2=29
172)
A)
B)
C)
D)
Find the equation in standard form of an ellipse centered at the origin that passes through the given points.
173)
(–3 2, 0), (3 2, 0), (0, –2), and (0, 2)
173)
A)
18x2+2y2= 1
B)
x2
2+y2
18 = 1
C)
x2
3 2 +y2
2= 1
D)
x2
18 +y2
2= 1
Identify the equation as a parabola, circle, ellipse, or hyperbola.
174)
x2–3y =9
174)
A)
Parabola
B)
Ellipse
C)
Circle
D)
Hyperbola
82
Write the equation in standard form. Then identify the vertex of the parabola.
175)
x = 2y2+ 3y – 9
175)
A)
x =2y +3
22– 9; –9, –3
4
B)
x =2y +3
42–81
8; –81
8, 3
4
C)
x =y +3
22–27
2; –27
2, –3
2
D)
x =2y +3
42–81
8; –81
8, –3
4
Solve.
176)
x2+y2=24
y2= 2x +16
176)
A)
(3, 2 5), (–4, 2 2), (3, –2 5), (–4, –2 2)
B)
(2, 2 5), (–3, 2 2), (2, –2 5), (–3, –2 2)
C)
(2, 21), (–4, 21), (2, –21), (–4, –21)
D)
(2, 2 5), (–4, 2 2), (2, –2 5), (–4, –2 2)
Graph.
177)
y = –2x2+ 8x – 4
177)
A)
B)
83
C)
D)
84
Solve the nonlinear inequality.
178)
(x + 4)2+ (y + 1)29
178)
A)
B)
C)
D)
85
Graph.
179)
2y2+ 2x2=98
179)
A)
B)
C)
D)
Solve the problem.
180)
If a rock is thrown vertically upward from the top of a building 144 feet high with an initial velocity
of 128 feet per second, the height, h, above ground level after t seconds is given by h = –16t2+128t
+144, where h is in feet and t is in seconds. How many seconds will it take the rock to reach its
maximum height?
180)
A)
9 sec
B)
3 sec
C)
8 sec
D)
4 sec
86
Solve.
181)
x2+ y2=85
x – y =1
181)
A)
(7, 6), (–6, –7)
B)
(–7, 6), (–6, 7)
C)
(–7, –6), (–6, –7)
D)
(7, –6), (6, –7)
Solve the nonlinear inequality.
182)
x2+ y29
182)
A)
B)
C)
D)
87
Solve the problem.
183)
Using a radio navigation system, it is determined that a ship is located on the hyperbola
x2
1311 –y2
22,513 = 1. If the ship is 90 miles offshore, find the coordinates of the ship’s location, to the
nearest tenth.
90 mi
183)
A)
(90, 1.2)
B)
(1.4, 90)
C)
(1.2, 8100)
D)
(1.2, 90)
Find the center and radius of the the circle.
184)
x2+ y2=100
184)
A)
Center: (0, 0);
Radius: 10
B)
Center: (10, 10);
Radius: 100
C)
Center: (0, 0);
Radius: 100
D)
Center: (0, 0);
Radius: 10
Find the distance between the two points on the coordinate plane. If necessary, round the answer to the nearest
thousandth.
185)
(–7, 5) and (–2, 17)
185)
A)
565 units 23.770 units
B)
13 units
C)
119 units 10.909 units
D)
403 units 20.075 units
Solve the problem.
186)
The sum of the squares of two numbers is 221 and the difference of their squares is 21. Find the two
numbers
186)
A)
B)
C)
D)
Solve.
187)
y =x2+ 4
y = 2x2+ 2
187)
A)
(–2, 2), ( 2, 2)
B)
(–2, 6), ( 2, 6)
C)
( 2, 6)
D)
(–2, 2, ( 2, 6)
88
Solve the problem.
188)
The owner of a cosmetics store determines that her weekly revenue R (in dollars) for selling x
bottles of lotion is given by R = –(x –45)2+2025. Identify the vertex of the parabola and explain its
significance in this situation.
188)
A)
B)
C)
D)
Find the distance between the two points on the coordinate plane. If necessary, round the answer to the nearest
thousandth.
189)
(–5, –4) and (6, –2)
189)
A)
9 units
B)
117 units
C)
117 13 units 421.849 units
D)
5 5 units 11.180 units
Find the equation in standard form of the parabola whose graph is shown.
190)
190)
A)
y = –x2+ 1
B)
x = –y2+ 1
C)
x =y2+ 1
D)
x = –y2– 1
Solve the nonlinear inequality.
191)
16x2+y2>256
191)
89
A)
B)
C)
D)
Identify the equation as a parabola, circle, ellipse, or hyperbola.
192)
9x2+ 16y2=144
192)
A)
Ellipse
B)
Parabola
C)
Circle
D)
Hyperbola
90
Graph.
193)
y = (x – 6)2+ 3
193)
A)
B)
C)
D)
Find the midpoint of the line segment joining the pair of points.
194)
(–5, –4) and (4, 4)
194)
A)
–9
2, – 4
B)
–1
2, 0
C)
(–9, –8)
D)
(–1, 0)
Solve the nonlinear inequality.
91
195)
y x2+ 2x + 5
195)
A)
B)
C)
D)
Solve.
196)
y =12x –x2
y =4x + 15
196)
A)
(5, 35), (3, 27)
B)
(5, 3)
C)
(–5, 35), (–3, 27)
D)
(–5, –5), (–3, 3)
Graph.
92
197)
9y2– 36x2=324
197)
A)
B)
C)
D)
93
198)
(x + 5)2+y2=1
198)
A)
B)
C)
D)
94
Answer Key
Testname: C12
95
Answer Key
Testname: C12
96
Answer Key
Testname: C12
97
Answer Key
Testname: C12
98