Question

Enter the x-intercepts of the quadratic function in the boxes. f(x) = x^2 + 4x - 60?

show the work and answer please

Answer 1

(-10, 0) and (6, 0).

Explanation:

Set f(x) = x² + 4x - 60 = to 0 and solve for x to answer this question.

Using "completing the square" to find the roots:

f(x) = x² + 4x - 60 = 0

= x² + 4x + 4 - 4 - 64 = 0

Rewriting x² + 4x + 4 as the square of a binomial, we get:

f(x) = (x + 2)² - 4 - 60 = 0, or

(x + 2)² = 64

Taking the square root of both sides, we get:

x + 2 = ±√64 = ±√64 = ±8

Then x = -2 + 8, or 6, and x = -2 - 8, or -10.

The x-intercepts of this function are (-10, 0) and (6, 0).

Answer 2

X-intercepts are where the parabola touches the x-axis so are the roots. (X^2)+4x-60=0 ; (x-6)(x+10) =0; x-6=0 so x=6 and x+10=0 so x=-10.