Find the x intercepts of the parabola with vertex (5,-12) and y intercept (0,63)

The equation for the standard form of parabola is given as:

y = A (x - h)^2 + k

with (h, k) being the (x, y) coordinates of the vertex

For the given problem, we are given that (h, k) = (5, - 12).
We can then use point (0, 63) for x and y to solve for A
63 = A (0 - 5)^2 - 12
75 = A (25)

A =  75 / 25

A = 3

Equation of given parabola: 
y = 3 (x - 5)^2 - 12

We can now solve for the x –intercept:
Set y = 0, then solve for x

0 = 3 (x - 5)^2 - 12

3 (x - 5)^2 = 12

(x - 5)^2 = 4

Taking sqrt of both sides
x - 5= ±2

x = -2 - 5 = -7 and x = 2 - 5 = - 3
x = -3, -7

x-intercepts of given parabola: -3 and -7

(-3, 0) and (-7, 0)