Find the Maximum/Minimum Value m(x)=-2x^2+6x+9

Math
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 parentheses.
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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Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Multiply .
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Multiply by .
Multiply by .
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 .
Cancel the common factor of .
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Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Find the common denominator.
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Write as a fraction with denominator .
Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
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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Add and .
Add and .
The final answer is .
Use the and values to find where the maximum occurs.
Find the Maximum/Minimum Value m(x)=-2x^2+6x+9
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