# Find the Maximum/Minimum Value f(x)=4x^2-9x-7

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 .
Multiply by .
Move the negative in front of the fraction.
Multiply .
Multiply by .
Multiply by .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply .
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 .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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.
Multiply by .
Subtract from .
Move the negative in front of the fraction.