# Math Help - Finding the correct equation for a parobola

1. ## Finding the correct equation for a parobola

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

Attempted Solution:

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

I plugged in the vertex.

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

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

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

(-1,0) is on the parabola ...

$0 = a(-1 - 3)^2 - 6$

$0 = 16a - 6$

$a = \frac{3}{8}$

(7,0) is on the parabola ...

$0 = a(7 - 3)^2 - 6$

$0 = 16a - 6$

wow ... same value for "a".