Algebra 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 .
Tap for more steps...
Step 2.1
Substitute in the values of and .
Step 2.2
Remove parentheses.
Step 2.3
Simplify .
Tap for more steps...
Step 2.3.1
Multiply by .
Step 2.3.2
Move the negative in front of the fraction.
Step 2.3.3
Multiply .
Tap for more steps...
Step 2.3.3.1
Multiply by .
Step 2.3.3.2
Multiply by .
Step 3
Evaluate .
Tap for more steps...
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Tap for more steps...
Step 3.2.1
Simplify each term.
Tap for more steps...
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 .
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
Step 3.2.4.1
Multiply by .
Step 3.2.4.2
Multiply by .
Step 3.2.5
Simplify the expression.
Tap for more steps...
Step 3.2.5.1
Subtract from .
Step 3.2.5.2
Add and .
Step 3.2.5.3
Move the negative in front of the fraction.
Step 3.2.6
The final answer is .
Step 4
Use the and values to find where the minimum occurs.
Step 5
Enter YOUR Problem
Mathway requires javascript and a modern browser.