Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Move to the left of .

Multiply by .

Subtract from .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Subtract from .

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 .

Move the negative one from the denominator of .

Multiply.

Multiply by .

Multiply by .

Replace the variable with in the expression.

Simplify each term.

Raise to the power of .

Multiply by .

Multiply by .

Simplify by adding and subtracting.

Add and .

Subtract from .

The final answer is .

Use the and values to find where the maximum occurs.

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