Question

write an equation of a parabola with a vertex at the origin and a directx at y=5

Answer 1

Directrix at y=5 (horizontal line) → The parabola is vertical
Vertex at the orgin: V=(0,0)=(h,k)→h=0, k=0
The directix is above the vertex→the parabola opens downward→p is negative
p is the distance between the vertex and the directrix→p=-5
Equation has the form:
(x-h)^2=4p(y-k)
(x-0)^2=4(-5)(y-0)
x^2=-20y