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
Answer:
x-intercepts of given parabola: -3 and -7
(-3, 0) and (-7, 0)