# Precalculus Examples

Step 1

To find the coordinate of the vertex, set the inside of the absolute value equal to . In this case, .

Step 2

Step 2.1

Add to both sides of the equation.

Step 2.2

Divide each term in by and simplify.

Step 2.2.1

Divide each term in by .

Step 2.2.2

Simplify the left side.

Step 2.2.2.1

Cancel the common factor of .

Step 2.2.2.1.1

Cancel the common factor.

Step 2.2.2.1.2

Divide by .

Step 2.2.3

Simplify the right side.

Step 2.2.3.1

Cancel the common factor of and .

Step 2.2.3.1.1

Factor out of .

Step 2.2.3.1.2

Cancel the common factors.

Step 2.2.3.1.2.1

Factor out of .

Step 2.2.3.1.2.2

Cancel the common factor.

Step 2.2.3.1.2.3

Rewrite the expression.

Step 3

Replace the variable with in the expression.

Step 4

Step 4.1

Cancel the common factor of .

Step 4.1.1

Factor out of .

Step 4.1.2

Cancel the common factor.

Step 4.1.3

Rewrite the expression.

Step 4.2

Subtract from .

Step 4.3

The absolute value is the distance between a number and zero. The distance between and is .

Step 5

The absolute value vertex is .

Step 6