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
Step 2.1
Substitute in the values of and .
Step 2.2
Remove parentheses.
Step 2.3
Simplify .
Step 2.3.1
Cancel the common factor of and .
Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Cancel the common factors.
Step 2.3.1.2.1
Factor out of .
Step 2.3.1.2.2
Cancel the common factor.
Step 2.3.1.2.3
Rewrite the expression.
Step 2.3.1.2.4
Divide by .
Step 2.3.2
Multiply by .
Step 3
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
Raise to the power of .
Step 3.2.1.2
Multiply by .
Step 3.2.2
Simplify by adding and subtracting.
Step 3.2.2.1
Subtract from .
Step 3.2.2.2
Add and .
Step 3.2.3
The final answer is .
Step 4
Use the and values to find where the minimum occurs.
Step 5