Question

Find the x-intercepts of the parabola with
vertex (7,-12) and y-intercept (0,135).

Answer 1

x=9 and x=5

OR

(9,0) and (5,0)

Explanation:

Use vertex form to solve for the unknown variable

`y=a(x-h)^2+k\\\\135=a(0-7)^2-12\\\\147=a(-7)^2\\\\147=49a\\\\3=a`

Use the new equation to find the x-intercepts

`y=3(x-7)^2-12\\\\0=3(x-7)^2-12\\\\12=3(x-7)^2\\\\4=(x-7)^2`

`2=x-7\\9=x`

`-2=x-7\\5=x`

Therefore, the x-intercepts of the parabola are (9,0) and (5,0). Feel free to review the attached graph for more information.