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.

Cancel the common factor.

Rewrite the expression.

Replace the variable with in the expression.

Simplify each term.

Apply the product rule to .

One to any power is one.

Raise to the power of .

Combine and .

Combine and .

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.

Find the Maximum/Minimum Value f(x)=3x^2-3x