# Precalculus Examples

Step 1

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

occurs at

Step 2

Substitute in the values of and .

Remove parentheses.

Simplify .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Step 3

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Raising to any positive power yields .

Multiply by .

Add and .

The final answer is .

Step 4

Use the and values to find where the minimum occurs.

Step 5