,

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 .

Raise to the power of .

Move to the left of .

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

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

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

Remove parentheses.

Simplify each term.

Subtract from .

Rewrite as .

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 (2,1) with Vertex (0,5) (0,5) , (2,1)