# Find the Maximum/Minimum Value g(x)=-(x-2)^2-3 Simplify each term.
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.
Simplify .
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 the result.
Simplify each term.
Raise to the power of .
Multiply by .
Multiply by .
Simplify by adding and subtracting.
Subtract from .
The final answer is .
Use the and values to find where the maximum occurs.
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