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Algebra Examples
Step 1
Combine and .
Step 2
The maximum of a quadratic function occurs at . If is negative, the maximum value of the function is .
occurs at
Step 3
Step 3.1
Substitute in the values of and .
Step 3.2
Remove parentheses.
Step 3.3
Simplify .
Step 3.3.1
Multiply by .
Step 3.3.2
Cancel the common factor.
Step 3.3.2.1
Dividing two negative values results in a positive value.
Step 3.3.2.2
Cancel the common factor of .
Step 3.3.2.2.1
Cancel the common factor.
Step 3.3.2.2.2
Rewrite the expression.
Step 3.3.3
Multiply by .
Step 4
Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
Step 4.2.1
Combine the numerators over the common denominator.
Step 4.2.2
Simplify each term.
Step 4.2.2.1
Multiply by by adding the exponents.
Step 4.2.2.1.1
Multiply by .
Step 4.2.2.1.1.1
Raise to the power of .
Step 4.2.2.1.1.2
Use the power rule to combine exponents.
Step 4.2.2.1.2
Add and .
Step 4.2.2.2
Raise to the power of .
Step 4.2.3
Add and .
Step 4.2.4
Simplify each term.
Step 4.2.4.1
Multiply by .
Step 4.2.4.2
Divide by .
Step 4.2.5
Add and .
Step 4.2.6
The final answer is .
Step 5
Use the and values to find where the maximum occurs.
Step 6