,

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 .

Subtract from .

Simplify each term.

Multiply by .

Raise to the power of .

Move to the left of .

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

Add to both sides of the equation.

Add and .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Divide by .

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

Remove parentheses.

Simplify .

Simplify each term.

Multiply by .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Move to the left of .

Multiply by .

Add and .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

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 (0,8) with Vertex (-1.5,-12.5) (-1.5,-12.5) , (0,8)