# Precalculus Examples

Rewrite the equation in vertex form.

Complete the square for .

Use the form , to find the values of , , and .

Consider the vertex form of a parabola.

Substitute the values of and into the formula .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Divide by .

Find the value of using the formula .

Simplify each term.

Raising to any positive power yields .

Multiply by .

Divide by .

Multiply by .

Add and .

Substitute the values of , , and into the vertex form .

Set equal to the new right side.

Use the vertex form, , to determine the values of , , and .

Since the value of is positive, the parabola opens up.

Opens Up

Find the vertex .

The range of a parabola that opens up starts at its vertex and extends to infinity.

Interval Notation:

Set-Builder Notation: