Question

Which is the standard form of the equation of the parabola that has a vertex of (–4, –6) and a directrix of y = 3?
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Answer 1

Vertex (h,k) = (−4,−6). Directrix y = 3 is 9 units above the vertex, so p = −9 (focus at (−4,−15)) and the parabola opens downward. Standard vertex form for a vertical parabola:

(x − h)^2 = 4p(y − k)

So

(x + 4)^2 = 4(−9)(y + 6) = −36(y + 6).