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

Since there is no variable to replace, the result is .

The absolute value vertex is .

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

Set-Builder Notation:

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Simplify the numerator.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Move the negative in front of the fraction.

is approximately which is negative so negate and remove the absolute value

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Simplify the numerator.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Move the negative in front of the fraction.

is approximately which is negative so negate and remove the absolute value

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply and .

Multiply by .

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Simplify the numerator.

Write as a fraction with a common denominator.

Combine the numerators over the common denominator.

Add and .

is approximately which is positive so remove the absolute value

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply and .

Multiply by .

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Simplify the numerator.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

is approximately which is positive so remove the absolute value

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

The final answer is .

The absolute value can be graphed using the points around the vertex

Graph y=1/2|x+2/3|+7