Explanation:
To find the x-intercepts of the quadratic function f(x) = x^2 + 6x - 27, we need to set f(x) equal to zero and solve for x.
So we have:
f(x) = 0
x^2 + 6x - 27 = 0
We can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 6, and c = -27.
Substituting these values into the quadratic formula, we get:
x = (-6 ± sqrt(6^2 - 4(1)(-27))) / 2(1)
x = (-6 ± sqrt(180)) / 2
x = (-6 ± 6sqrt(5)) / 2
x = -3 ± 3sqrt(5)
So the x-intercepts of the quadratic function are approximately -10.16 and 4.16.