Question 350003
Refer to the standard form for a parabola:   (x-h)^2 = 4a*(y-k)   vertex of parabola is at (h,k)  focus is at (h, k + a).
directrix at y= k - a

we have y = -2 = k - a   and  -5 = k + a,  with h = 3

-2 = k - a
-5 = k + a

-7 = 2k

k = -7/2

vertex at (3, -7/2)

a = -5 - k = -5 - (-7/2) = -3/2


equation is :  (x -3)^2 = 4*(-3/2)*(y - (-7/2))

Equation: (x-3)^2 = -6(y + 7/2)