Posted by **samantha** on Sunday, June 15, 2008 at 7:35pm.

6. Find the equation of each parabola described below.

a) parabola with vertex (0,0) and the focus (0,7)

b) parabola with focus (-3,0) and directrix x=3

c) parabola with vertex (3,3) and directrix x=-1

d) parabola with focus (-2,-1) and directrix y=5

e) ysquared=-6x translated according to ((x,y) -->(x-2,y+4))

could someone help me with these??

- algebra -
**Damon**, Sunday, June 15, 2008 at 9:27pm
You need to know the following:

vertex at (h,k)

if it opens up or down:

4 a (y-k) = (x-h)^2

a negative a opens down

if it opens right or left:

4 a (x-h) = (y-k)^2

a negative a opens left

distance vertex to focus = a

distance vertex to directrix = a

ALWAYS SKETCH THEM

================================

for example a is vertex (0,0) so h = k = 0 and focus (0,7)

the sketch shows it with axis along the y axis opening up and distance a = 7

so

4 * 7 * y = x^2

or y = x^2/28

- algebra -
**Damon**, Sunday, June 15, 2008 at 9:29pm
Note that the vertex is halfway between the focus and the directrix by the way.

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