162
CHAPTER 6, FORM E
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
1. The graph of the equation
214 51x y y= – +
is a parabola. Find 2. ____________
the coordinates of its vertex and the equation of its axis.
a. Vertex:
17
,
22
æö
÷
ç÷
ç÷
ç
èø
; axis:
7
2
y=
b. Vertex:
( )
2, 7
; axis:
c. Vertex:
7
2, 2
æö
÷
ç÷
ç÷
ç
èø
; axis:
d. Vertex:
11
,
22
æö
÷
ç–÷
ç÷
ç
èø
; axis:
1
2
y=-
3. The graph of the equation
2
6yx=
is a parabola. Find 3. ____________
the coordinates of its focus and equation of its directrix.
a. Focus:
3
0, 2
æö
÷
ç–÷
ç÷
ç
èø
; directrix:
1
2
x=
b. Focus:
1
0, 24
æö
÷
ç÷
ç÷
ç
èø
; directrix:
1
24
y=-
c. Focus:
3
0, 2
æö
÷
ç÷
ç÷
ç
èø
; directrix:
1
2
y=
d. Focus:
1
0, 24
æö
÷
ç–÷
ç÷
ç
èø
; directrix:
1
24
x=
4. Write an equation for the parabola with vertex (–1, –8), 4. ____________
passing through the point (–3, –16), and opening downward.
a.
2
8 2( 1)xy+ = – +
b.
2
8 2( 1)xy+ = +
c.
2
8 2( 1)yx+ = – +
d.
2
8 2( 1)yx+ = +
5. Write an equation for the ellipse centered at the origin having 5. ____________
a vertical major axis of length 28 and a minor axis of length 12.
a.
22
1
14 6
xy
+=
b.
22
1
196 36
xy
+=
c.
22
1
6 14
xy
+=
d.
22
1
36 196
xy
+=
163
CHAPTER 6, FORM E
6. Find an equation of the hyperbola with x-intercepts ±4 and foci at 7. ____________
(0, 65) and (0, – 65)
.
a.
22
1
16 81
xy
-=
b.
22
1
81 16
xy
-=
c.
22
1
49 16
xy
-=
d.
22
1
16 49
xy
-=
7. An arch in the shape of the top half of an ellipse 6. ____________
is 2 m wide and 6 m high at the center. Find the height
of the arch .5 m from the center of the bottom.
(Round your answer to two decimal places.)
a. 5.50 m b. 5.35 m
c. 5.20 m d. 5.05 m
Identify the type of graph defined by each equation.
8.
21
9 25
yx
-=
8. ____________
a. Ellipse b. Hyperbola
c. Parabola d. No graph
9.
22
9
2
yx
–=-
9. ____________
a. Ellipse b. Circle
c. Parabola d. Hyperbola
10.
22
4 6 13 0x x y y– + – + =
10. ____________
a. Ellipse b. Point
c. Circle d. No graph
11.
22
16 4 64xy=+
12. ____________
a. Ellipse b. Point
c. Circle d. Hyperbola
12.
22
2 2 0x x y y– + – =
11. ____________
a. Ellipse b. Point
c. Circle d. No graph
13.
22
10 5yx+=
13. ____________
a. Ellipse b. No graph
c. Circle d. Hyperbola
CHAPTER 6, FORM E
164
14. Which of the following would be a function used to graph 14. ____________
the equation
22
1
16 25
xy
-=
using a graphing calculator?
a.
2
151 16
x
y=-
b.
2
151
16
x
y=-
c.
2
151
16
x
y=+
d.
2
151
16
x
y= – +
Match the equation with its graph.
15.
22
( 2) ( 2) 1
9 16
xy+-
+=
16.
____________
a.
b.
c.
d.
CHAPTER 6, FORM E
165
16.
2
( 2)xy=-
15. ____________
a.
b.
c.
d.
17.
22
9 36 4xy=-
17. ____________
a.
b.
c.
d.
CHAPTER 6, FORM E
166
18.
22
( 4) 1
99
yx–
-=
19. ____________
a.
b.
c.
d.
19.
2
1
2 16
yx
=+
18. ____________
a.
b.
c.
d.
CHAPTER 6, FORM E
167
20.
22
16yx=-
20. ____________
a.
b.
c.
d.
168
CHAPTER 6, FORM E