SOLUTION: I do not understand how to solve this problem: Write the equation of the parabola with vertex (-2,-2) and directrix y=0. I know that the form should be y=a(x-k)^2+k and that

Question 192645: I do not understand how to solve this problem:
Write the equation of the parabola with vertex (-2,-2) and directrix y=0.
I know that the form should be y=a(x-k)^2+k
and that it should be a(x+2)^2-2
but I don't get how to get the a.
Answer to problem is: -(1/8)(x+2)^2-2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Write the equation of the parabola with vertex (-2,-2) and directrix y=0.
I know that the form should be y=a(x-k)^2+k
and that it should be a(x+2)^2-2
but I don't get how to get the a.
Answer to problem is: -(1/8)(x+2)^2-2
-------------------------------------------
Starting with (x-h)^2 = 4p(y-k)
Since the vertex is (-2,-2) you get
(x+2)^2 = 4p(y+2)
-----------------------
Since the directrix is the x-axis and the vertex is 2 below it, p = -2
So (x+2)^2 = 4(-2)(y+2)
-------------
Solving for y you get:
-8(y+2) = (x+2)^2
y = (-1/8)(x+2)^2 -2
==============================
Cheers,
Stan H.

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