Apply the distributive property.

Multiply by by adding the exponents.

Move .

Multiply by .

Multiply by .

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.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Replace the variable with in the expression.

Simplify each term.

Multiply by by adding the exponents.

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Multiply by .

Simplify by adding and subtracting.

Subtract from .

Add and .

The final answer is .

Use the and values to find where the minimum occurs.

Find the Maximum/Minimum Value g(x)=2x(x-4)+7