# Finite Math Examples

Find the Maximum/Minimum Value
Step 1
The minimum of a quadratic function occurs at . If is positive, the minimum value of the function is .
occurs at
Step 2
Find the value of .
Substitute in the values of and .
Remove parentheses.
Multiply by .
Step 3
Evaluate .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Multiply by .
Raise to the power of .
Raise to the power of .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply .
Multiply by .
Combine and .
Multiply by .
Move the negative in front of the fraction.
Find the common denominator.
Multiply by .
Multiply by .
Write as a fraction with denominator .
Multiply by .
Multiply by .
Reorder the factors of .
Multiply by .
Combine the numerators over the common denominator.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Subtract from .
Move the negative in front of the fraction.
Step 4
Use the and values to find where the minimum occurs.
Step 5