Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the equation with the correct graph.
1)
x2+ y2+ 4x + 12y + 24 = 0
1)
A)
B)
C)
D)
1
2)
x =2y2– 8y + 3
2)
A)
B)
C)
D)
2
3)
(x + 6)2+ (y – 4)2=4
3)
A)
B)
C)
D)
3
4)
x2+ y2– 12x – 10y + 52 = 0
4)
A)
B)
C)
D)
4
5)
(x – 2)2+ (y + 1)2=49
5)
A)
B)
C)
D)
5
6)
y = (x + 6)2+ 2
6)
A)
B)
C)
D)
6
7)
x = (y + 4)2– 5
7)
A)
B)
C)
D)
7
8)
y2
16 –x2
64 = 1
8)
A)
B)
C)
D)
8
9)
x2
64 –y2
36 = 1
9)
A)
B)
C)
D)
9
10)
x2
9+y2
16 = 1
10)
A)
B)
C)
D)
10
11)
y =3x2+ 12x + 9
11)
A)
B)
C)
D)
Graph the solution set of the system of inequalities.
12)
x2
36 + y2
9 1
x2 + y29
12)
11
A)
B)
C)
D)
Provide an appropriate response.
13)
If the x–intercepts of an ellipse are (–6, 0) and (6, 0) and the y–intercepts are (0, 3) and (0, –3) what
is the equation of the ellipse?
13)
A)
x2
36 –y2
9= 1
B)
x2
9+y2
36 = 1
C)
y2
9–x2
36 = 1
D)
x2
36 +y2
9= 1
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
14)
y = x2– 2x + 2
14)
12
A)
opens up; vertex (–1, 3);
axis of symmetry x = –1
B)
opens up; vertex (1, 1);
axis of symmetry x =1
C)
opens up; vertex (1, –3);
axis of symmetry x =1
D)
opens up; vertex (–1, 1);
axis of symmetry x = –1
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Sketch the graph.
15)
(x + 3)2+ (y – 2)2=16
15)
13
A)
B)
C)
D)
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Do not graph.
16)
5x2+ 2x – 9 – y = 0
16)
A)
ellipse
B)
circle
C)
hyperbola
D)
parabola
Find the center and radius and draw the graph.
17)
(x + 5)2+ (y – 5)2=4
17)
14
A)
center (-5, 5); radius 2
B)
center (5, -5); radius 2
C)
center (-5, -5); radius 2
D)
center (5, 5); radius 2
Graph the inequality.
18)
x2
9+y2
16
1
18)
15
A)
B)
C)
D)
Solve the problem.
19)
A railroad tunnel is shaped like a semi–ellipse. The height of the tunnel at the center is 45 ft and the
vertical clearance must be 18 ft at a point 21 ft from the center. Find an equation for the ellipse.
19)
A)
x2
525 +y2
324 = 1
B)
x2
2025 +y2
525 = 1
C)
x2
525 +y2
2025 = 1
D)
x2
441 +y2
2025 = 1
Provide an appropriate response.
20)
Do the points that lie on the boundary curve solve the inequality 4x2–25y2<100?
20)
A)
Yes
B)
No
21)
Complete the following: The set of all points that are 8 units from the point whose coordinates are
(2, 4) is a with and .
21)
A)
circle; center at (2, 4); radius 8
B)
circle; center at (2, 4); radius 64
C)
circle; center at (0, 0); radius 8
D)
parabola; vertex at (2, 4); opens up
Graph the solution set of the system of inequalities.
16
22)
x2
16 + y2
49 1
x2 + y249
y x
22)
A)
B)
C)
D)
The coordinates of the center of a circle and a point on the circle are given. Find the radius of the circle.
23)
Center: (-1, 0), point on the circle: (-1, 2)
23)
A)
4
B)
2
C)
–2
D)
0
Find the center and radius and draw the graph.
17
24)
x2+ y2– 12x – 2y + 33 = 0
24)
A)
center (6, -1); radius 2
B)
center (-6, 1); radius 2
C)
center (6, 1); radius 2
D)
center (-6, -1); radius 2
The center and radius of a circle are given. Write the equation of each circle in standard form.
25)
Center: (-7, 4), r =5
25)
A)
(x – 4)2+ (y + 7)2=25
B)
(x + 7)2+ (y – 4)2=5
C)
(x + 4)2+ (y – 7)2=25
D)
(x – 7)2+ (y + 4)2=5
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
18
26)
x = (y – 3)2– 5
26)
A)
opens right; vertex (–3, 5);
axis of symmetry y =5
B)
opens right; vertex (-5, 3);
axis of symmetry y =3
C)
opens right; vertex (-5, –3);
axis of symmetry y = –3
D)
opens right; vertex (3, -5);
axis of symmetry y =-5
Find the center and radius and draw the graph.
19
27)
x2+ y2+ 10x + 6y + 18 = 0
27)
A)
center (-5, 3); radius 4
B)
center (5, -3); radius 4
C)
center (5, 3); radius 4
D)
center (-5, -3); radius 4
20
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Sketch the graph.
28)
x2+ y2=9
28)
A)
B)
C)
D)
Use the given information to write the equation of the circle in standard form.
29)
Center: (-8, 3), point on the circle (–14, 11)
29)
A)
(x + 8)2+(y – 3)2=10
B)
(x – 8)2+(y + 3)2=10
C)
(x – 8)2+(y + 3)2=100
D)
(x + 8)2+(y – 3)2=100
21
Solve the problem.
30)
A Ferris wheel has a diameter of 340 feet and the bottom of the Ferris wheel is 14 feet above the
ground. Find the equation of the wheel if the origin is placed on the ground directly below the
center of the wheel, as illustrated.
340 ft
14 ft
30)
A)
x2+(y – 170)2=28,900
B)
x2+(y – 184)2=28,900
C)
x2+y2=28,900
D)
x2+(y – 170)2=115,600
Use a graphing calculator to solve the system of equations.
31)
y = 5x2
2y – 5x = –12
31)
A)
(1, 5)
B)
(0, 0)
C)
(0, –6)
D)
No solution
The center and radius of a circle are given. Write the equation of each circle in standard form.
32)
Center: (7, 0), r =14
32)
A)
(x + 7)2+ y2=14
B)
x2+ (y + 7)2=196
C)
(x – 7)2+ y2=14
D)
x2+ (y – 7)2=196
Graph the inequality.
33)
x2
36 –y2
49 > 1
33)
22
A)
B)
C)
D)
Graph the hyperbola and label all intercepts.
34)
25y2– 4x2=100
34)
23
A)
(–2, 0), (2, 0)
B)
(0, 5), (0, –5)
C)
(0, 2), (0, –2)
D)
(–5, 0), (5, 0)
Provide an appropriate response.
35)
Is x2+ y2+ 12x + 18y + 53 = 0 the equation of a circle or parabola?
35)
A)
Circle
B)
Parabola
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Do not graph.
36)
4y2– 16x2=64
36)
A)
ellipse
B)
circle
C)
hyperbola
D)
parabola
Find the midpoint between the two points.
37)
(4, 2) and (3, 0)
37)
A)
(1, 2)
B)
1
2, 1
C)
7
2, 1
D)
(7, 2)
The center and radius of a circle are given. Write the equation of each circle in standard form.
38)
Center: (0, 5), r =2
38)
A)
x2+ (y + 5)2=2
B)
(x + 5)2+ y2=4
C)
(x – 5)2+ y2=4
D)
x2+ (y – 5)2=4
24
Solve the system of equations.
39)
x2 + y2 = 9
y = x2 – 3
39)
A)
(0, –3), ( 5, 2)
B)
(0, 3), ( 5, 2)
C)
(–5, 2), (0, –3), ( 5, 2)
D)
No solution
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Sketch the graph.
40)
x2
9–y2
16 = 1
40)
A)
B)
C)
D)
Provide an appropriate response.
41)
Would the graph of the inequality 16x2–64y21024 be drawn solid or dashed?
41)
A)
Solid
B)
Dashed
Graph the inequality.
25
42)
x2
4+y2
36 > 1
42)
A)
B)
C)
D)
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
26
43)
x = –(y + 1)2+ 6
43)
A)
opens left; vertex (-1, 6);
axis of symmetry y =6
B)
opens left; vertex (6, -1);
axis of symmetry y =-1
C)
opens left; vertex (6, 1);
axis of symmetry y =1
D)
opens left; vertex (1, -6);
axis of symmetry y =-6
Solve the system of equations.
44)
x2 + y2 = 85
x – y = 1
44)
A)
(7, 6), (–6, -7)
B)
(-7, 6), (–6, 7)
C)
(-7, –6), (–6, -7)
D)
(7, –6), (6, -7)
27
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Do not graph.
45)
25y2+ 9x2=225
45)
A)
parabola
B)
hyperbola
C)
ellipse
D)
circle
Find the center and radius and draw the graph.
46)
(x – 3)2+ (y – 3)2=36
46)
A)
center (3, -3); radius 6
B)
center (-3, 3); radius 6
C)
center (-3, -3); radius 6
D)
center (3, 3); radius 6
Find the distance between the two points.
47)
(3, -4) and (7, -6)
47)
A)
2 5
B)
12 3
C)
6
D)
12
28
Solve the system of equations.
48)
x2 + y2 = 49
x2 – y2 = 49
48)
A)
(7, 7), (-7, 7)
B)
(7, 0), (-7, 0)
C)
(7, 0), (7, 7)
D)
No solution
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
49)
y = (x + 2)2+ 3
49)
A)
opens up; vertex (–3, 2);
axis of symmetry x = –3
B)
opens up; vertex (2, 3);
axis of symmetry x =2
C)
opens up; vertex (3, –2);
axis of symmetry x =3
D)
opens up; vertex (–2, 3);
axis of symmetry x = –2
29
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Do not graph.
50)
x2+y2–4x –16y + 64 = 0
50)
A)
hyperbola
B)
ellipse
C)
parabola
D)
circle
Solve the system of equations.
51)
y = 6x2
6x + y = –12
51)
A)
(–2, 0)
B)
(0, 0)
C)
(1, 6)
D)
No solution
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Sketch the graph.
52)
(x – 4)2+ (y + 1)2=36
52)
A)
B)
C)
D)
30
53)
y = –3x2+ 12x – 7
53)
A)
B)
C)
D)
Provide an appropriate response.
54)
Would the graph of the inequality 36y2–9x2>324 be drawn solid or dashed?
54)
A)
Solid
B)
Dashed
Solve the system of equations.
55)
7x2 – y2 = 21
y = x2 – 3
55)
A)
(–10, 7), ( 10, 7)
B)
(0, –3), (0, 3), (7, –10), (7, 10)
C)
(–3, 0), ( 3, 0)
D)
(–3, 0), ( 3, 0), (–10, 7), ( 10, 7)
Graph the solution set of the system of inequalities.
31
56)
x2
16 – y2
49 1
x2
49 + y2
16 1
56)
A)
B)
C)
D)
32
57)
x – y 1
x + 4y 16
y –x2 + 5
57)
A)
B)
C)
D)
Solve the problem.
58)
If a rock is thrown vertically upward from the top of a building 80 feet high with an initial velocity
of 64 feet per second, the height, h, above ground level after t seconds is given by h = –16t2+64t +
80, where h is in feet and t is in seconds. How many seconds will it take the rock to hit the ground?
58)
A)
1 sec
B)
4 sec
C)
2 sec
D)
5 sec
Graph the ellipse. Label the x– and y–intercepts.
33
59)
x2+y2
25 = 1
59)
A)
no x–intercepts;
y–intercepts: (0, 5), (0, –5)
B)
x–intercepts: (–1, 0), (1, 0);
y–intercepts: (0, 5), (0, –5)
C)
x–intercepts: (–5, 0), (5, 0);
no y–intercepts
D)
x–intercepts: (–5, 0), (5, 0);
y–intercepts: (0, 1), (0, –1)
Find the midpoint between the two points.
60)
(2, -2) and (-9, 2)
60)
A)
– 7
2, 0
B)
(11, -4)
C)
(-7, 0)
D)
11
2, – 2
Provide an appropriate response.
61)
Is x2– 2x – 4 + y = 0 the equation of a circle or parabola?
61)
A)
Circle
B)
Parabola
34
The coordinates of the center of a circle and a point on the circle are given. Find the radius of the circle.
62)
Center: (3, –5), point on the circle: (6, –9)
62)
A)
25
B)
4
C)
3
D)
5
Graph the ellipse. Label the x– and y–intercepts.
63)
49x2+4y2=196
63)
A)
x–intercepts:(–7, 0), (7, 0);
y–intercepts: (0, 3), (0, –3)
B)
x–intercepts:(–7, 0), (7, 0);
y–intercepts: (0, 2), (0, –2)
C)
x–intercepts: (–2, 0), (2, 0);
y–intercepts: (0, 7), (0, –7)
D)
x–intercepts:(–7, 0), (7, 0);
y–intercepts: (0, 8), (0, –8)
Find the distance between the two points.
64)
(5, 1) and (-2, -4)
64)
A)
35
B)
2
C)
2 6
D)
74
35
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
65)
x = –y2– 4y + 3
65)
A)
opens left; vertex (1, 2);
axis of symmetry y =2
B)
opens right; vertex (– 1, 2);
axis of symmetry y =2
C)
opens left; vertex (7, -2);
axis of symmetry y =-2
D)
opens left; vertex (1, -2);
axis of symmetry y =-2
Graph the solution set of the system of inequalities.
36
66)
y > x2– 5
2y – x < 2
66)
A)
B)
C)
D)
Solve the system of equations.
67)
xy = 9
x2 + y2 = 18
67)
A)
(3, –3), (–3, 3)
B)
(3, 3)
C)
(–3, –3), (3, 3)
D)
No solution
Find the midpoint between the two points.
68)
(-8, -7) and (4, 2)
68)
A)
(-12, -9)
B)
– 2, – 5
2
C)
(-4, -5)
D)
– 6, – 9
2
37
The coordinates of the center of a circle and a point on the circle are given. Find the radius of the circle.
69)
Center: (-2, -4), point on the circle (6, 2)
69)
A)
2 3
B)
2 7
C)
10
D)
2 5
Find the distance between the two points.
70)
(3, 5) and (15, 0)
70)
A)
119
B)
299
C)
349
D)
13
Graph the solution set of the system of inequalities.
71)
x2
9 – y2
25 1
x2
49 + y2
9 1
y – x 2
71)
A)
B)
38
C)
D)
Solve the problem.
72)
If a satellite reaches a speed of 7.91 kilometers per second, it will attain a circular orbit. If a satellite
is placed in an orbit of 220 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)?
72)
A)
x2+y2=167,961,600
B)
x2+y2=48,400
C)
x2+y2= 40,576,900
D)
x2+y2=43,428,100
Solve the system of equations.
73)
2x = y2
x2 + y2 = 48
73)
A)
(6, –2 3), (6, 2 3)
B)
(6, 2 3), (–8, 4)
C)
(6, –2 3), (6, 2 3), (–8, –4), (–8, 4)
D)
No solution
Provide an appropriate response.
74)
How many real solutions are possible for a system of equations whose graphs are a parabola and
an ellipse?
74)
A)
0, 1, 2, or 3 solutions
B)
1, 2, 3, or 4 solutions
C)
0, 1, 2, 3, or 4 solutions
D)
0, 1, 2, 3, 4, or 5 solutions
39
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Sketch the graph.
75)
x = y2+ 3
75)
A)
B)
C)
D)
Graph the hyperbola and label all intercepts.
40
76)
y2
4–x2
64 = 1
76)
A)
(0, 2), (0, –2)
B)
(–8, 0), (8, 0)
C)
(0, 8), (0, –8)
D)
(–2, 0), (2, 0)
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
41
77)
x =2(y – 2)2– 2
77)
A)
opens right; vertex (–2, 2);
axis of symmetry y =2
B)
opens left; vertex (2, 2);
axis of symmetry y =2
C)
opens right; vertex (–2, –2);
axis of symmetry y = –2
D)
opens right; vertex (2, 2);
axis of symmetry y =2
Solve the system of equations.
78)
y = x2– 10x + 25
x + y = 11
78)
A)
(5, 6)
B)
(7, 18), (2, 9)
C)
(7, 4), (2, 9)
D)
(-7, 18), (-2, 13)
Graph the hyperbola and label all intercepts.
42
79)
x2
4–y2
25 = 1
79)
A)
(–2, 0), (2, 0)
B)
(0, 2), (0, –2)
C)
(–5, 0), (5, 0)
D)
(0, 5), (0, –5)
Find the center and radius and draw the graph.
43
80)
(x – 4)2+ (y + 5)2=16
80)
A)
center (-4, -5); radius 4
B)
center (-4, 5); radius 4
C)
center (4, -5); radius 4
D)
center (4, 5); radius 4
44
Solve the problem.
81)
An elliptical trainer is an exercise machine in which your foot moves in an elliptical path. On a
typical machine, the length of the stride is about 25 inches and the height is varies from 2 to 6
inches depending on the settings. Write the equation for the path your foot takes if the total length
of the stride is 25 inches and the total height is 2 inches.
25 inches 2 inches
81)
A)
x2
1+y2
156.25 = 1
B)
x2
156.25 +y2
1= 1
C)
x2
625 +y2
4= 1
D)
x2
25 +y2
2= 1
Graph using a graphing calculator.
82)
(x – 6)2
9+(y + 5)2
16 = 1
(scl = 2)
(scl = 2)
82)
A)
45
B)
C)
D)
Provide an appropriate response.
83)
Which direction does the parabola, x=-2y2+ 18y+ 5, open?
83)
A)
Left
B)
Down
C)
Right
D)
Up
Graph the solution set of the system of inequalities.
46
84)
x2 + y24
x2 + y225
84)
A)
B)
C)
D)
The coordinates of the endpoints of a diameter are given. Find the equation of the circle.
85)
(6, -8), (2, -6)
85)
A)
(x + 4)2+(y – 7)2=5
B)
(x – 4)2+(y + 7)2=5
C)
(x – 4)2+(y + 7)2=10
D)
(x + 4)2+(y – 7)2=10
Graph using a graphing calculator.
47
86)
y2
20 +x2
72 = 1
(scl = 2)
(scl = 2)
86)
A)
(scl = 2)
(scl = 2)
B)
(scl = 2)
(scl = 2)
C)
(scl = 2)
(scl = 2)
D)
(scl = 2)
(scl = 2)
Graph the solution set of the system of inequalities.
48
87)
x2
9 + y2
4< 1
y > x2 – 2
87)
A)
B)
C)
D)
Graph the inequality.
49
88)
x2+ y2<25
88)
A)
B)
C)
D)
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
50
89)
x =3y2– 18y + 26
89)
A)
opens right; vertex (1, 3);
axis of symmetry y =3
B)
opens left; vertex (-1, 3);
axis of symmetry y =3
C)
opens right; vertex (-1, 3);
axis of symmetry y =3
D)
opens right; vertex (-1, -3);
axis of symmetry y =-3
51
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Sketch the graph.
90)
y =4(x – 1)2– 3
90)
A)
B)
C)
D)
The center and radius of a circle are given. Write the equation of each circle in standard form.
91)
Center: (9, 0), r =2
91)
A)
x2+ (y – 9)2=2
B)
(x – 9)2+ y2=4
C)
x2+ (y + 9)2=2
D)
(x + 9)2+ y2=4
Use a graphing calculator to solve the system of equations.
92)
y = (x – 2)2 + 4
y = -(x – 1)2 + 5
92)
A)
(1, 5)
B)
(2, 4)
C)
(2, 4), (1, 5)
D)
No solution
52
Solve.
93)
The sum of the squares of two numbers is 58 and the difference of their squares is 40. Find the two
numbers
93)
A)
3 and 7
B)
3 and 7; 3 and –7
C)
3 and 7; –3 and –7
D)
3 and 7; 3 and –7; –3 and 7; –3 and –7
Graph using a graphing calculator.
94)
x2+ y2=100
(scl = 2)
(scl = 2)
94)
A)
B)
53
C)
D)
Provide an appropriate response.
95)
How can you tell the equation of an ellipse from the equation of the hyperbola?
95)
A)
B)
C)
D)
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Sketch the graph.
96)
x2
4+y2
9= 1
96)
54
A)
B)
C)
D)
Solve the system of equations.
97)
3x2– 5y2 = -68
2x2+ 5y2 = 88
97)
A)
(2, 4), (4, 2), (-2, -4), (-4, -2)
B)
(2, -4), (2, 4)
C)
(2, 4), (-2, 4), (2, -4), (-2, -4)
D)
(-2, -4), (-4, -2)
Graph the inequality.
98)
x2
16 –y2
4< 1
98)
55
A)
B)
C)
D)
Use the given information to write the equation of the circle in standard form.
99)
The set of all points that are a distance of 3 units from (1, 9).
99)
A)
(x + 1)2+ (y + 9)2=9
B)
(x + 9)2+ (y + 1)2=3
C)
(x – 9)2+ (y – 1)2=3
D)
(x – 1)2+ (y – 9)2=9
Solve the system of equations.
100)
x2 + y2 = 22
y2 = 2x + 19
100)
A)
(1, 21), (-3, 13), (1, –21), (-3, –13)
B)
(1, 21), (-2, 13), (1, –21), (-2, –13)
C)
(2, 21), (-3, 13), (2, –21), (-3, –13)
D)
No solution
Graph using a graphing calculator.
56
101)
x2
16 –y2
64 = 1
(scl = 2)
(scl = 2)
101)
A)
B)
C)
57
D)
Solve the system of equations.
102)
10y2 – x2 = 1
xy = 3
102)
A)
(–3, –1)
B)
(3, 1), (–3, –1)
C)
(3, 1)
D)
No solution
The center and radius of a circle are given. Write the equation of each circle in standard form.
103)
Center: (–4, –6), r =9
103)
A)
(x – 6)2+ (y – 4)2=9
B)
(x + 6)2+ (y + 4)2=9
C)
(x – 4)2+ (y – 6)2=81
D)
(x + 4)2+ (y + 6)2=81
Provide an appropriate response.
104)
How many real solutions are possible for a system of equations whose graphs are an ellipse and a
hyperbola (both centered at the origin)?
104)
A)
0, 1, 2, 3, or 4 solutions
B)
0, 1, 2, or 3 solutions
C)
0, 2, or 4 solutions
D)
2 or 4 solutions
Graph the solution set of the system of inequalities.
105)
x2 + y281
2x + y 3
105)
58
A)
B)
C)
D)
106)
x – y -1
x + 4y 19
y5
106)
59
A)
B)
C)
D)
Graph using a graphing calculator.
107)
(x + 1)2+ (y – 4)2=16
(scl = 2)
(scl = 2)
107)
60
A)
(scl = 2)
(scl = 2)
B)
(scl = 2)
(scl = 2)
C)
(scl = 2)
(scl = 2)
D)
(scl = 2)
(scl = 2)
Graph the ellipse. Label the x– and y–intercepts.
108)
x2
4+y2
25 = 1
108)
61
A)
x–intercepts: (–2, 0), (2, 0);
no y–intercepts
B)
x–intercepts: (–2, 0), (2, 0);
y–intercepts: (0, 5), (0, –5)
C)
x–intercepts: (–5, 0), (5, 0);
y–intercepts: (0, 2), (0, –2)
D)
no x–intercepts;
y–intercepts: (0, 5), (0, –5)
Solve the system of equations.
109)
2x2– 4y2 = 16
3x2+ 4y2 = 64
109)
A)
(4, -2), (4, 2)
B)
(4, 2), (2, 4), (-4, -2), (-2, -4)
C)
(4, 2), (-4, 2), (4, -2), (-4, -2)
D)
(-4, -2), (-2, -4)
Graph the inequality.
110)
y2
36 –x2
9< 1
110)
62
A)
B)
C)
D)
Provide an appropriate response.
111)
If a hyperbola opens up and down and the vertices of the fundamental rectangle are (2, 5), (2, –5),
(–2, 5) and (–2, –5), what is the equation of the hyperbola?
111)
A)
y2
25 –x2
4= 1
B)
y2
4–x2
25 = 1
C)
x2
25 –y2
4= 1
D)
x2
4–y2
25 = 1
Solve the system of equations.
112)
x2 + y2 = 1
x + y = -1
112)
A)
(0, -1), (1, 0)
B)
(0, 1), (-1, 0)
C)
(0, -1), (-1, 0)
D)
(0, 1), (1, 0)
63
Solve the problem.
113)
Arches in the shapes of parabolas are often used in construction. Find the equation of a parabolic
arc that is 22 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.
22 ft
30 ft
113)
A)
y = –x2+ 22
B)
y = –x2+ 30
C)
y = – 22
225x2+ 22
D)
y =22
225x2+ 22
114)
If a rock is thrown vertically upward from the top of a building 112 feet high with an initial velocity
of 96 feet per second, the height, h, above ground level after t seconds is given by h = –16t2+96t +
112, where h is in feet and t is in seconds. How many seconds will it take the rock to reach its
maximum height?
114)
A)
6 sec
B)
7 sec
C)
2 sec
D)
3 sec
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
115)
x = –3y2+ 12y – 7
115)
64
A)
opens right; vertex (5, 2);
axis of symmetry y =2
B)
opens left; vertex (-5, 2);
axis of symmetry y =2
C)
opens left; vertex (5, –2);
axis of symmetry y = –2
D)
opens left; vertex (5, 2);
axis of symmetry y =2
Use a graphing calculator to solve the system of equations.
116)
y = x2+ 10x + 26
y = –x2– 6x – 8
116)
A)
(-3, 1)
B)
(-5, 1), (-3, 1)
C)
(-5, 1)
D)
No solution
Graph the ellipse. Label the x– and y–intercepts.
117)
x2
16 +y2= 1
117)
65
A)
x–intercepts: (–4, 0), (4, 0);
no y–intercepts
B)
x–intercepts: (–1, 0), (1, 0);
y–intercepts: (0, 4), (0, –4)
C)
x–intercepts: (–4, 0), (4, 0);
y–intercepts: (0, 1), (0, –1)
D)
no x–intercepts;
y–intercepts: (0, 4), (0, –4)
Solve the system of equations.
118)
64x2 + 9y2 = 576
3y – 8x = 24
118)
A)
(0, 8), (-3, 0)
B)
(0, 3), (0, -8)
C)
(0, -8), (3, 0)
D)
(0, -3), (8, 0)
The center and radius of a circle are given. Write the equation of each circle in standard form.
119)
Center: (0, -1), r =13
119)
A)
(x – 1)2+ y2=169
B)
x2+ (y + 1)2=13
C)
(x + 1)2+ y2=169
D)
x2+ (y – 1)2=13
Solve the problem.
66
120)
A comet has an orbit that is in the shape of an ellipse with the Sun at one of the foci. The equation is
approximately x2
4.52 + y2
3.32 = 1, where x and y are in astronomical units (an astronomical unit is
93,000,000 miles). Sketch the graph of the comet.
120)
A)
B)
C)
D)
Provide an appropriate response.
121)
In the definitions of the ellipse and hyperbola, two fixed points are mentioned. What are these
points called?
121)
A)
intercepts
B)
foci
C)
vertices
D)
asymptotes
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
67
122)
x =-3(y – 5)2+ 4
122)
A)
opens right; vertex (4, 5);
axis of symmetry y =5
B)
opens left; vertex (4, 5);
axis of symmetry y =5
C)
opens right; vertex (– 4, 5);
axis of symmetry y =5
D)
opens left; vertex (– 4, 5);
axis of symmetry y =5
Find the center and radius and draw the graph.
68
123)
(x + 1)2+ (y + 4)2=16
123)
A)
center (1, -4); radius 4
B)
center (1, 4); radius 4
C)
center (-1, -4); radius 4
D)
center (-1, 4); radius 4
Find the midpoint between the two points.
124)
(-5, 5) and (–2, 4)
124)
A)
– 3
2, 1
2
B)
(–7, 9)
C)
(-3, 1)
D)
–7
2, 9
2
Provide an appropriate response.
125)
Is y2– 2y + 1 –x = 0 the equation of a circle or parabola?
125)
A)
Circle
B)
Parabola
69
Solve.
126)
Find the dimensions of a rectangular enclosure with perimeter 58 yd and area 190 yd2.
126)
A)
10 yd by 18 yd
B)
10 yd by 19 yd
C)
11 yd by 19 yd
D)
11 yd by 18 yd
Provide an appropriate response.
127)
Find the coordinates of the vertex of the parabola y =2x2+ 12x + 19.
127)
A)
(-3, 1)
B)
(3, 1)
C)
(-3, – 1)
D)
(1, -3)
Find the distance between the two points.
128)
(–2, -3) and (6, 1)
128)
A)
4
B)
48 3
C)
48
D)
4 5
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Sketch the graph.
129)
y2
4–x2
25 = 1
129)
A)
B)
C)
D)
The coordinates of the endpoints of a diameter are given. Find the equation of the circle.
130)
(–3, 1), (-9, –7)
130)
A)
(x – 6)2+(y – 3)2= 25
B)
(x + 6)2+(y + 3)2= 25
C)
(x + 6)2+(y + 3)2= 5
D)
(x – 6)2+(y – 3)2= 100
70
Solve the problem.
131)
A whispering gallery is a room in the shape of an elliptic reflector. If a source of sound is placed at
one focal point of an elliptic reflector, the sound is reflected through the other focal point. If one
person speaks at one focal point, then another person at the other can hear sounds as faint as a
whisper. If the whispering gallery is based on the ellipse x2
25 + y2
9 = 1, how many units from the
center of the ellipse would the two people stand?
131)
A)
16 units
B)
5 units
C)
3 units
D)
4 units
Solve.
132)
The area of a rectangular rug is 140 square feet and its perimeter is 48 feet. Find the dimensions of
the rug.
132)
A)
11 yd by 14 yd
B)
10 yd by 14 yd
C)
11 yd by 13 yd
D)
10 yd by 13 yd
Find the distance between the two points.
133)
(-7, -7) and (1, –3)
133)
A)
48 3
B)
4 5
C)
4
D)
48
Solve the system of equations.
134)
16x2 – 16y2 = 256
16x2 + 9y2 = 144
134)
A)
(0, 4), (0, –4)
B)
(–4, 0), (4, 0)
C)
(–3, 0), (3, 0)
D)
No solution
135)
x2 + y2 = 29
x2 – y2 = -21
135)
A)
(2, -5), (2, 5)
B)
(2, 5), (5, 2), (-2, -5), (-5, -2)
C)
(2, 5), (-2, 5), (2, -5), (-2, -5)
D)
(-2, -5), (-5, -2)
Provide an appropriate response.
136)
If a hyperbola opens left and right and the vertices of the fundamental rectangle are (3, 6), (3, –6), (–
3, 6) and (–3, –6), what is the equation of the hyperbola?
136)
A)
y2
9–x2
36 = 1
B)
x2
36 –y2
9= 1
C)
x2
9–y2
36 = 1
D)
y2
36 –x2
9= 1
The coordinates of the endpoints of a diameter are given. Find the equation of the circle.
137)
(–8, –9), (1, 4)
137)
A)
x – 7
2
2+y – 5
2
2=74
B)
x + 7
2
2+y + 5
2
2=125
2
C)
x – 7
2
2+y + 5
2
2=218
D)
x + 9
2
2+y + 13
2
2=250
Graph using a graphing calculator.
71
138)
y2
25 –x2
49 = 1
(scl = 2)
(scl = 2)
138)
A)
B)
C)
72
D)
Provide an appropriate response.
139)
How many real solutions are possible for a system of equations whose graphs are a line and
a hyperbola?
139)
A)
1, 2, or 3 solutions
B)
1 or 2 solutions
C)
0, 1, or 2 solutions
D)
0, 1, 2, or 3 solutions
Graph the inequality.
140)
y2
49 –x2
4
1
140)
A)
B)
73
C)
D)
Solve the problem.
141)
In a certain state, the percent of deaths by age per million miles driven can be approximated by the
equation y = 0.0068x2 – 0.5321x + 10.642, where x is the age and y is the percent. Find the percent of
deaths per million miles for drivers 30 years old.
141)
A)
0.799%
B)
0.238%
C)
55.879%
D)
32.725%
Find the midpoint between the two points.
142)
(8, –2) and (6, 2)
142)
A)
(14, 0)
B)
7, 2
C)
7, –2
D)
7, 0
Graph the hyperbola and label all intercepts.
143)
9x2– 16y2=144
143)
A)
(0, 3), (0, –3)
B)
(–4, 0), (4, 0)
74
C)
(–3, 0), (3, 0)
D)
(0, 4), (0, –4)
Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. Sketch the graph.
144)
x = (y + 4)2+ 2
144)
A)
B)
75
C)
D)
Find the midpoint between the two points.
145)
(6, 1) and (–6, 4)
145)
A)
(0, 5)
B)
–6, 5
2
C)
6, 5
2
D)
0, 5
2
Find the direction the parabola opens, the coordinates of the vertex, the equation of the axis of symmetry and draw the
graph.
146)
x = y2– 2y + 4
146)
A)
opens down; vertex (-1, 5);
axis of symmetry x =-1
B)
opens right; vertex (3, -1);
axis of symmetry y =-1
76
C)
opens right; vertex (3, 1);
axis of symmetry y =1
D)
opens up; vertex (1, 3);
axis of symmetry x =1
Graph using a graphing calculator.
147)
x2
4+y2
49 = 1
(scl = 2)
(scl = 2)
147)
A)
77
B)
C)
D)
78
Graph the inequality.
148)
y > (x + 5)2– 3
148)
A)
B)
C)
D)
79
149)
y <4(x + 3)2+ 3
149)
A)
B)
C)
D)
150)
x2+ y225
150)
80
A)
B)
C)
D)
Provide an appropriate response.
151)
Do the points that lie on the boundary curve solve the inequality 49x2–25y21225?
151)
A)
Yes
B)
No
Solve the problem.
152)
A wildlife researcher is monitoring a black bear that has a radio telemetry collar with a transmitting
range of 29 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?
152)
A)
x2–y2=29
B)
x2+y2=29
C)
x2+y2=58
D)
x2+y2=841
Solve the system of equations.
153)
y = 11x – x2
2x – y = –20
153)
A)
(4, 5)
B)
(4, 28), (5, 30)
C)
(–4, 12), (–5, 10)
D)
No solution
Graph the ellipse. Label the x– and y–intercepts.
81
154)
16x2+49y2=784
154)
A)
x–intercepts: (–4, 0), (4, 0);
y–intercepts: (0, 7), (0, –7)
B)
x–intercepts: (–7, 0), (7, 0);
y–intercepts: (0, 8), (0, –8)
C)
x–intercepts: (–7, 0), (7, 0);
y–intercepts: (0, 4), (0, –4)
D)
x–intercepts: (–7, 0), (7, 0);
y–intercepts: (0, 5), (0, –5)
Graph using a graphing calculator.
82
155)
(x – 6)2+ (y + 1)2=16
(scl = 2)
(scl = 2)
155)
A)
(scl = 2)
(scl = 2)
B)
(scl = 2)
(scl = 2)
C)
(scl = 2)
(scl = 2)
D)
(scl = 2)
(scl = 2)
Solve the problem.
156)
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?
156)
A)
112 ft.
B)
400 ft.
C)
144 ft.
D)
160 ft.
83
Answer Key
Testname: C11
84
Answer Key
Testname: C11
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Answer Key
Testname: C11
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Answer Key
Testname: C11
87