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 parentheses.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply .

Multiply by .

Multiply by .

Replace the variable with in the expression.

Simplify each term.

Apply the product rule to .

Raise to the power of .

Raise to the power of .

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Find the common denominator.

Write as a fraction with denominator .

Multiply by .

Multiply and .

Write as a fraction with denominator .

Multiply by .

Multiply and .

Combine fractions.

Combine fractions with similar denominators.

Multiply.

Multiply by .

Multiply by .

Simplify the numerator.

Add and .

Add and .

The final answer is .

Use the and values to find where the maximum occurs.

Find the Maximum/Minimum Value m(x)=-2x^2+6x+9