Answer:
[tex]y=-\frac{1}{8}x^2[/tex]
Step-by-step explanation:
Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2
The distance between the focust and the directrix is the value of 2p
Distance beween focus (0,-2) and y=2 is 4
[tex]2p=4, p=2[/tex]
The distance between vertex and focus is p that is 2
Focus is at (0,-2) , so the vertex is at (0,0)
General form of equation is
[tex]y-k=-\frac{1}{4p}(x-h)^2[/tex]
where (h,k) is the vertex
Vertex is (0,0) and p = 2
The equation becomes
[tex]y-0=-\frac{1}{4(2)}(x-0)^2[/tex]
[tex]y=-\frac{1}{8}x^2[/tex]
