# Thread: Help with finding the equation of a parabola

1. ## Help with finding the equation of a parabola

Hi,

Could someone explain how you work through this kind of sums:

"A parabola has x-axis intercepts 6 and -3 and passes through the point (1, 10). Find the equation of the Parabola"

Any help would be much appreciated,

Thanks,

Dru

2. You have the following points (1,10),(-3,0) & (6,0)

Use the general form $y= a(x-h)^2+k$ and sub these points in, then solve for a,h and k.

Here's a start

(1,10): $10= a(1-h)^2+k$

(-3,0): $0= a(-3-h)^2+k$

(6,0): $0= a(6-h)^2+k$

3. You could even use $y=ax^2+bx+c$ and sub these points in.

You would have to solve the following system

$10 = a+b+c$
$0= 9a-3b+c$
$0=36a+6b+c$