168
CHAPTER 6, FORM F
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
1. The graph of the equation
2
22x y y=+
is a parabola. Find 2. ____________
the coordinates of its vertex and the equation of its axis.
a. Vertex:
11
,
22
æö
÷
ç–÷
ç÷
ç
èø
; axis:
1
2
x=-
b. Vertex:
11
,
22
æö
÷
ç–÷
ç÷
ç
èø
; axis:
1
2
y=
c. Vertex:
11
,
22
æö
÷
ç–÷
ç÷
ç
èø
: axis:
1
2
y=-
d. Vertex:
11
,
22
æö
÷
ç–÷
ç÷
ç
èø
; axis:
1
2
x=
2. Describe the parabola which is the graph of the equation 1. ____________
2
( 2) 2( 3)yx+ = – –
a. Vertex at (3, –2), opening to the left
b. Vertex at (–2, 3), opening to the right
c. Vertex at (1, 2), opening downward
d. Vertex at (1, –2), opening upward
3. The graph of the equation
2
1
2
xy=-
is a parabola. Find 3. ____________
the coordinates of its focus and equation of its directrix.
a. Focus:
1
1, 9
æö
÷
ç–÷
ç÷
ç
èø
; directrix:
1
2
y=-
b. Focus:
1
9, 9
æö
÷
ç÷
ç÷
ç
èø
; directrix:
1
2
y=
c. Focus:
1, 0
2
æö
÷
ç–÷
ç÷
ç
èø
; directrix:
1
2
x=
d. Focus:
( )
1, 9—
; directrix:
11x=-
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+ = +
169
CHAPTER 6, FORM F
5. Find an equation of the hyperbola with x-intercepts ±4 and foci at 7. ____________
(0, 65) and (0, – 65)
.
a.
22
1
49 16
xy
-=
b.
22
1
16 49
xy
-=
c.
22
1
81 16
xy
-=
d.
22
1
16 81
xy
-=
6. Write an equation for the ellipse centered at the origin having 5. ____________
a vertical major axis of length 12 and a minor axis of length 6.
a.
22
1
36 9
xy
+=
b.
22
1
9 36
xy
+=
c.
22
1
6 12
xy
+=
d.
22
1
12 6
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. 5.20 m b. 5.05 m
c. 5.50 m d. 5.35 m
Identify the type of graph defined by each equation.
11.
22
6 36 6xy=-
11. ____________
a. Parabola b. Circle
c. Ellipse d. Hyperbola
9.
22
4 4 8xy+=
9. ____________
a. Parabola b. Circle
c. Ellipse d. Point
10.
22
16 36 1xy=+
10. ____________
a. Parabola b. Circle
c. Ellipse d. Hyperbola
8.
22
25 2yx=-
8. ____________
a. Parabola b. Hyperbola
c. Ellipse d. No graph
170
CHAPTER 6, FORM F
12.
22
5xy= – –
12. ____________
a. Parabola b. Circle
c. Ellipse d. No graph
13.
22
49xy-=
13. ____________
a. Parabola b. Hyperbola
c. Ellipse d. No graph
14. Which of the following would be a function used to graph 14. ____________
the equation
22
1
25 16
xy
-=
using a graphing calculator?
a.
2
141 25
x
y=-
b.
2
141
25
x
y=+
c.
2
141
25
x
y=-
d.
2
141
25
x
y= – +
Match the equation with its graph.
15.
( )
2
35xy= – – +
15. ____________
a.
b.
c.
d.
171
CHAPTER 6, FORM F
16.
22
1
16 9
xy
-=
16. ____________
a.
b.
c.
d.
17.
22
16 25 400xy+=
17. ____________
a.
b.
c.
d.
172
CHAPTER 6, FORM F
18.
22
9 36 4xy=+
18. ____________
a.
b.
c.
d.
19.
22
99xy=-
19. ____________
a.
b.
c.
d.
173
CHAPTER 6, FORM F
20.
2
16yx=-
20. ____________
a.
b.
c.
d.
174
CHAPTER 6, FORM F