Question

A parabola with vertex (1,-16) and y-intercept (0,-15) crosses the x-axis in two places. One x-intercept is at (5,0). Find the other x-intercept.

Answer 1

(-3,0) is the other x-intercept

Explanation:

We know that the equation for the vertex form of a parabola is y=a(x-h)^2+k where (h,k) is the vertex.

Given (h,k) -> (1,-16) then we have y=(x-1)^2-16 as our equation.

Given that one x-intercept is at (5,0) we can plug in y=0 to find both:

0=(x-1)^2-16

0=x^2-2x+1-16

0=x^2-2x-15

0=(x-5)(x+3)

x=5 and x=-3

Therefore, the other x-intercept is (-3,0)