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CHAPTER 6, FORM D
COLLEGE ALGEBRA
NAME
DATE
Graph each parabola. Give the domain, range, vertex, and axis.
1.
2
3 – 6x y y=
1. vertex : __________________________
axis : __________________________
2.
2
26y 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
2
16xy=
. directrix : __________________________
4. Write an equation for the parabola with vertex (– 4, 2), 4. _______________________________
passing through the point (41, 5), and opening to the left.
5. A radio telescope has a diameter of 80 feet and a maximum 5. _______________________________
depth of 6 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.
159
CHAPTER 6, FORM D
Graph each ellipse. Give the domain and range.
6.
22
9 25 225xy+=
6.
7.
2
2
( 3) 1
9
y
x+ + =
7.
8. a.
Graph
2
1
59
xy
=-
.
8. a.
b. Tell whether the graph is that of a function. b. ___________________________
9. Write an equation for the ellipse centered at (–8, 5) having 9. ______________________________
a horizontal major axis of length 22 and a minor axis of
length 12.
CHAPTER 6, FORM D
160
10. An arch in the shape of the top half of an ellipse is 4 ft 10. _______________________________
wide and 3 ft high at the center. Find the height of the
arch 1 ft from the center of the bottom. (Round your
answer to two decimal places.)
Graph each hyperbola. Give the domain, range, and equations of
the asymptotes.
11.
22
25 9 225xy-=
11. domain:
range:
asymptotes :
12.
22
–1
49
xy
=
12. domain:
range :
asymptotes :
CHAPTER 6, FORM D
161
13. Find an equation of the hyperbola with center
(5, 3)
13. _______________________________
vertex at
(5, 6)
and passing through
(1, 8)
.
Identify the type of graph, if any, defined by each equation.
14.
2
2
41
16
y
x+=
14. _______________________________
15.
2
( 2) 3( 3)yx+ = – –
15. _______________________________
16.
22
1
16 16
xy
+=
16. _______________________________
17.
22
4( 2) 25( 4) 100yx+ – – =
17. _______________________________
18.
22
16( 6) 9( 4) 144xy– + – =
18. _______________________________
19.
2
( 5) 12( 4) 0xy+ + + =
19. _______________________________
20. Suppose the graph of the equation 20. _______________________________
22
1
16 100
xy
+=
is to be generated by a graphing calculator. What
two functions
12
and yy
would have to be used
to obtain the graph?
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CHAPTER 6, FORM D
164