Finite Math Examples

Find the Maximum/Minimum Value
The maximum or minimum of a quadratic function occurs at . If is negative, the maximum value of the function is . If is positive, the minimum value of the function is .
occurs at
Find the value of equal to .
Substitute in the values of and .
Remove the extra parentheses from the expression .
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Remove the parentheses from the numerator.
Remove the parentheses from the denominator.
Simplify .
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Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raising to any positive power yields .
Multiply by .
Add and .
The final answer is .
Use the and values to find where the minimum occurs.
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