Write an equation for a parabola with vertex (3, -6) crossing theThe Problem:x-axis at -1 and 7.

Attempted Solution:

The equation for a parobola is $\displaystyle y = a(x- h)^2 + k$.

I plugged in the vertex.

$\displaystyle y=a(x-3)^2 - 6$

I do not know how I would find what value would equal both -1 and 7, thought. There doesn't appear to be any algebric method which would work, at least to my intuitions.

Could someone please help?

Thank you