146
CHAPTER 6, FORM A
COLLEGE ALGEBRA
NAME
DATE
Graph each parabola. Give the domain, range, vertex, and axis.
1.
2
48x y y=+
1. vertex : __________________________
axis : __________________________
2.
2
28y x x=+
2. vertex : __________________________
axis : __________________________
3. Give the coordinates of the focus and the equation of the 3. focus : __________________________
directrix for the parabola with equation
212yx=
. directrix: __________________________
4. Write an equation for the parabola with vertex (–3, 2), 4. _______________________________
passing through the point (0, 4), and opening downward.
5. A radio telescope has a diameter of 120 feet and a maximum 5. _______________________________
depth of 20 feet. Find the equation of the parabola that models
models the cross section of the dish if the vertex is placed at the
origin and the parabola opens up.
147
CHAPTER 6, FORM A
Graph each ellipse. Give the domain and range.
6.
22
16 9 144xy+=
6.
7.
22
( 1) ( 2) 1
16 9
xy+-
+=
7.
8. a.
Graph
2
– 1– .
3 25
yx
=
8. a.
b. Tell whether the graph is that of a function. b. ___________________________
9. Write an equation for the ellipse centered at the origin 9. ______________________________
having a vertical minor axis of length 12 and a major axis
of length 24.
148
CHAPTER 6, FORM A
10. An arch in the shape of the top half of an ellipse is 10. _______________________________
14 ft wide and 2 ft high at the center. Find the width
of the arch between the points on the arch which are at a
height of 1 ft. (Round your answer to two decimal places.)
Graph each hyperbola. Give the domain, range, and equations of
the asymptotes.
11.
22
16 –16xy=
11. domain:
range:
asymptotes :
12.
22
1
4 16
yx
-=
12. domain:
range :
asymptotes :
13. Find the equation of the hyperbola with y–intercepts
7±
13. _______________________________
and foci at (0, 53) and (0, – 53).
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CHAPTER 6, FORM A
Identify the type of graph, if any, defined by each equation.
14.
22
6 2 8x x y y+ – + =
14. _______________________________
15.
22
6 4 – 24 0xy+=
15. _______________________________
16.
2
( 2) 8( 3)xy+ = – –
16. _______________________________
17.
22
( 2) ( 2) 1
49
xy+-
+=
17. _______________________________
18.
2
( 5) 4( 3)yx+ = –
18. _______________________________
19.
22
1
16 16
xy
+=
19. _______________________________
20. Suppose the graph of the equation 20. _______________________________
22
( 4) ( 5) 9xy+ + – =
is to be generated by a graphing calculator. What
two functions
12
and yy
would have to be used
to obtain the graph?
150
CHAPTER 6, FORM A
