Question

Find the x-intercepts of the parabola with

vertex (-3,405) and y-intercept (0,360).
Write your answer in this form: (X₁,Y₁), (X2,₂).
If necessary, round to the nearest hundredth.
Enter the correct answer.

Answer 1

Answer: (-12, 0) and (6, 0)

Explanation:

The equation of the parabola is of the form

`y=a(x+3)^2 + 405`. To find a, we can substitute in the coordinates (0,360).

`360=a(0+3)^2 + 405\\\\360=9a+405\\\\-45=9a\\\\a=-5`

So, the equation is
`y=-5(x+3)^2 + 405`. Setting this equal to 0,

`-5(x+3)^2 + 405=0\\\\5(x+3)^2 = 405\\\\(x+3)^2 = 81\\x+3=\pm 9\\\\x=-12, 6`

So, the x-intercepts are (-12, 0) and (6, 0).