Find the Maximum/Minimum Value f(x)=2x^2+3x-2

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.
Multiply by .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Multiply by .
Raise to the power of .
Raise to the power of .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply .
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Multiply by .
Combine and .
Multiply by .
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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Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps…
Multiply by .
Subtract from .
Move the negative in front of the fraction.
The final answer is .
Use the and values to find where the minimum occurs.
Find the Maximum/Minimum Value f(x)=2x^2+3x-2


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