# Finite Math Examples

The minimum of a quadratic function occurs at . If is positive, the minimum value of the function is .

occurs at

Substitute in the values of and .

Remove parentheses.

Simplify .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply .

Multiply by .

Multiply by .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Apply the product rule to .

One to any power is one.

Raise to the power of .

Combine and .

Combine and .

Move the negative in front of the fraction.

Find the common denominator.

Multiply by .

Multiply and .

Write as a fraction with denominator .

Multiply by .

Multiply and .

Multiply by .

Combine fractions.

Combine fractions with similar denominators.

Multiply by .

Simplify the numerator.

Subtract from .

Add and .

Move the negative in front of the fraction.

The final answer is .

Use the and values to find where the minimum occurs.