Question

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

Answer 1

Which way does the parabola opens?

Answer 2

Down?

Answer 3

the focus should help reveal how the parabola opens

Answer 4

good, so which general equation are you going to use?

Answer 5

y=a(x-h)^+k

Answer 6

you could, but it doesn't have a focus embedded in that equation. The better one is (x - h)^2 = 4p (y-k). Look familiar?

Answer 7

Oh is the answer y = -1/28x2

Answer 8

well, we'll see. Do you know what (h,k) and p stand for?

Answer 9

(H,k) is the vertex, nd p idk

Answer 10

p is the distance form the vertex to the focus. So what is that distance?

Answer 11

-7

Answer 12

technically it's 7. But because the parabola opens down, we know there will be a negative sign in front. So if you plug everything the general equation above, what do you get?

Answer 13

I got -1/28x2

Answer 14

how did you get that?

Answer 15

I just plugged in everything

Answer 16

ok, so you did (x - 0)^2 = -4(7)(y-0) right?

Answer 17

which then gave you y = -x^2/27 ?

Answer 18

28*

Answer 19

good