# Algebra 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 parentheses from the numerator.

Remove the parentheses from the denominator.

Multiply by .

Multiply by .

Replace the variable with in the expression.

Simplify each term.

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Raise to the power of .

Multiply by .

Raise to the power of .

Raise to the power of .

Cancel the common factor of .

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Simplify .

Multiply by .

Write as a fraction with denominator .

Multiply and .

Multiply by .

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 .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

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 .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

The final answer is .

Use the and values to find where the minimum occurs.