# Precalculus Examples

,

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 to get .

Rewrite the equation as .

Simplify the left side.

Simplify each term.

Subtract from to get .

Raise to the power of to get .

Move to the left of the expression .

Multiply by to get .

Add and to get .

Divide each term by and simplify.

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by to get .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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

Remove the extra parentheses.

Remove the parentheses around the expression .

Simplify each term.

Subtract from to get .

Remove parentheses around .

Simplify .

Write as a fraction with denominator .

Multiply and to get .

Add and to get .

The standard form and vertex form are as follows.

Standard Form:

Vertex Form:

Simplify the standard form.

Standard Form:

Vertex Form: