Precalculus Examples

Find the Maximum/Minimum Value
Find the x-value the minimum occurs at. Use this value to find the minimum value.
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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.
Multiply by to get .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Rewrite the expression.
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 .
One to any power is one.
Raise to the power of to get .
Simplify .
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Write as a fraction with denominator .
Multiply and to get .
Simplify .
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Write as a fraction with denominator .
Multiply and to get .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Multiply by to get .
Multiply by to get .
Subtract from to get .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by to get .
Multiply by to get .
Add and to get .
Move the negative in front of the fraction.
The final answer is .
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