Write then equation for a parabola with a focus at (0,-5) and a directrix at y=-3

Question

Write then equation for a parabola with a focus at (0,-5) and a directrix at y=-3

Answer 1

f(x)= y = -x^2-4

it's a downward opening parabola with vertex = (0,-4)

the y coordinate of the vertex is the midpoint between y=-3 and the y=-5 of the focus

average of -3 and -5 is -4

in vertex form

y=a(x-h)^2 + k where (h,k) is the vertex = (0,-4), h=0 and k =-4, so

y =a(x-0)^2 -4

y =ax^2 -4

a is negative since the parabola opens downward

y =-x^2 -4