write the equation of the parabola with an axis of symmetry of x=0; vertex (0,0); directrix y=4

Answer 1

A parabola follows the form ax² + bx + c where the vertex (h,k) = (-b/2a, k) = (0,0) --> -b/2a = 0 or b = 0, h = 0, and k = 0

To find the focus of a parabola, the following form is used where x-axis forms line of symmetry:

(x-h)² = 4p*(y-k) where the focus is (h,k+p) and directrix is y = k- p.

But h = 0 and k = 0--> focus = (0, p) and directrix y = -p = 4--> p = -4.

Therefore, (x-0)² = 4*-4(y-0) --> x² = -16y or y = -x²/16.