Precalculus Examples

Find the Maximum/Minimum Value
The minimum of a quadratic function occurs at . If is positive, the minimum value of the function is .
occurs at
Find the value of .
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Substitute in the values of and .
Remove parentheses.
Simplify .
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Multiply by .
Move the negative in front of the fraction.
Multiply .
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Multiply by .
Multiply by .
Evaluate .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Apply the product rule to .
Raise to the power of .
Raise to the power of .
Multiply .
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Combine and .
Multiply by .
Move the negative in front of the fraction.
Find the common denominator.
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Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
Multiply by .
Combine fractions.
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Combine fractions with similar denominators.
Multiply.
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Multiply by .
Multiply by .
Simplify the numerator.
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Subtract from .
Add and .
Move the negative in front of the fraction.
The final answer is .
Use the and values to find where the minimum occurs.
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