The x-intercepts of the parabola are (3, 0) and (7,0)
<h3>How to determine the x-intercept?</h3>The given parameters are:
Vertex (h, k) = (5, -12)
Point (x, y) = (0, 63)
The equation of a parabola is:
y = a(x - h)^2 + k
Substitute (h, k) = (5, -12)
y = a(x - 5)^2 - 12
Substitute (x, y) = (0, 63)
63 = a(0 - 5)^2 - 12
Evaluate
63 = 25a - 12
Add 12 to both sides
25a = 75
Divide by 26
a = 3
Substitute a = 3 in y = a(x - 5)^2 - 12
y = 3(x - 5)^2 - 12
Set y to 0 to determine the x-intercepts
0 = 3(x - 5)^2 - 12
Add 12 to both sides
3(x - 5)^2 = 12
Divide by 3
(x - 5)^2 = 4
Take the square root of both sides
Add 5 to both sides
Expand
x = (5 - 2, 5 + 2)
Evaluate
x = (3, 7)
Hence, the x-intercepts of the parabola are (3, 0) and (7,0)
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