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CHAPTER 6, FORM B
COLLEGE ALGEBRA
NAME
DATE
Graph each parabola. Give the domain, range, vertex, and axis.
1.
2
26x y y= – +
1. vertex : __________________________
axis : __________________________
2.
2
1( 2) 3
2
yx= – – +
2. vertex : __________________________
axis : __________________________
3. Give the coordinates of the focus and the equation of the 3. focus : __________________________
directrix for the parabola with equation
220xy=-
. directrix: __________________________
4. Write an equation for the parabola with vertex (4, 5), 4. _______________________________
passing through the point (0, 7), and opening upward.
5. A radio telescope has a diameter of 80 feet and a maximum 5. _______________________________
depth of 8 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.
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CHAPTER 6, FORM B
Graph each ellipse. Give the domain and range.
6.
22
9 225 25xy=-
6.
7.
22
( 3) 1
4 16
xy+
+=
7.
8. a.
Graph
2
1
2 25
yx
= – –
.
8. a.
b. Tell whether the graph is that of a function. b. ___________________________
9. Write an equation for the ellipse centered at (–4, 5) having 9. ______________________________
a vertical major axis of length 8 and a minor axis of length 4.
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CHAPTER 6, FORM B
10. An arch in the shape of the top half of an ellipse is 10. _______________________________
10 m wide and 4 m high at the center. Find the width
between the points on the arch which are at a height of 2 m.
(Round your answer to two decimal places.)
Graph each hyperbola. Give the domain, range, and equations of
the asymptotes.
11.
22
4 36 144yx– = –
11. domain:
range:
asymptotes :
12.
22
1
25 4
yx
-=
12. domain:
range :
asymptotes :
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CHAPTER 6, FORM B
13. Find an equation of the hyperbola with x-intercepts
4±
13. _______________________________
and the line with equation
3
4
yx=-
as an asymptote.
Identify the type of graph, if any, defined by each equation.
14.
2
( 1) 8( 2)xy– = +
14. _______________________________
15.
22
( 2) ( 4) 0
16 25
xy-+
+=
15. _______________________________
16.
22
4 9 16 18 11x y x y+ – – =
16. _______________________________
17.
22
2 4 12x y x y– – + =
17. _______________________________
18.
22
2 4 3 2 3x x y y+ = – –
18. _______________________________
19.
28 9 0x x y– + + =
19. _______________________________
20. Suppose the graph of the equation 20. _______________________________
22
( 3) ( 5) 1
4 36
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 B
156