,

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.

Multiply by .

Subtract from .

One to any power is one.

Multiply by .

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

Subtract from both sides of the equation.

Subtract from .

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 .

Rewrite as .

Rewrite as .

Multiply by .

Subtract from .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Add and .

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 (2,6) with Vertex (1,3) (1,3) , (2,6)