# Precalculus Examples

The maximum or minimum of a quadratic function occurs at . If is negative, the maximum value of the function is . If is positive, the minimum value of the function is .

occurs at

Find the value of equal to .

Substitute in the values of and .

Remove the extra parentheses from the expression .

Remove the parentheses from the numerator.

Remove the parentheses from the denominator.

Multiply by to get .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Rewrite the expression.

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Apply the product rule to .

One to any power is one.

Raise to the power of to get .

Simplify .

Write as a fraction with denominator .

Multiply and to get .

Simplify .

Write as a fraction with denominator .

Multiply and to get .

Move the negative in front of the fraction.

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Multiply by to get .

Multiply by to get .

Subtract from to get .

Move the negative in front of the fraction.

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Multiply by to get .

Add and to get .

Move the negative in front of the fraction.

The final answer is .