Hello, Frontier!

A parabola has x-intercepts at (-2, 0) and (6, 0).

Its maximum y-value is 12.

Write the standard form of the equation of this parabola. Did you make a sketch? Code:

| (2,12)
| *
*| : *
* | : *
* | : *
| :
- - * - - + - + - - - - * - -
-2 | 2 6

From the symmetry, we see that the vertex is at (2, 12).

The general equation of a parabola is: .

We know three points on the parabola: .

. . Use these point to create a system of equations.

Subtract: [2] - [1]: .

Subtract: [3] - [2]: .

Substitute [4]: .

Substitute [4] and [5] into [1]: .

Therefore: .

Edit: Dinkydoe has a much better solution!'.