,

The general equation of a parabola with vertex is . In this case we have as the vertex and is a point on the parabola. To find , substitute the two points in .

Rewrite the equation as .

Simplify each term.

Subtract from .

One to any power is one.

Multiply by .

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Add and .

Using , the general equation of the parabola with the vertex and is .

Remove parentheses.

Subtract from .

The standard form and vertex form are as follows.

Standard Form:

Vertex Form:

Simplify the standard form.

Standard Form:

Vertex Form:

Find the Parabola Through (1,-9) with Vertex (0,-6) (1,-9) , (0,-6)