# 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 .
Step 2.1
Substitute in the values of and .
Step 2.2
Remove parentheses.
Step 2.3
Simplify .
Step 2.3.1
Multiply by .
Step 2.3.2
Move the negative in front of the fraction.
Step 2.3.3
Multiply .
Step 2.3.3.1
Multiply by .
Step 2.3.3.2
Multiply by .
Step 3
Evaluate .
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Step 3.2.1
Simplify each term.
Step 3.2.1.1
Apply the product rule to .
Step 3.2.1.2
Raise to the power of .
Step 3.2.1.3
Raise to the power of .
Step 3.2.1.4
Multiply .
Step 3.2.1.4.1
Combine and .
Step 3.2.1.4.2
Multiply by .
Step 3.2.1.5
Move the negative in front of the fraction.
Step 3.2.2
Find the common denominator.
Step 3.2.2.1
Multiply by .
Step 3.2.2.2
Multiply by .
Step 3.2.2.3
Write as a fraction with denominator .
Step 3.2.2.4
Multiply by .
Step 3.2.2.5
Multiply by .
Step 3.2.2.6
Multiply by .
Step 3.2.3
Combine the numerators over the common denominator.
Step 3.2.4
Simplify each term.
Step 3.2.4.1
Multiply by .
Step 3.2.4.2
Multiply by .
Step 3.2.5
Simplify the expression.
Step 3.2.5.1
Subtract from .
Step 3.2.5.2