The function f of x is equal to negative open paren x minus 3 close paren squared plus 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x What is the maximum area of the rectangle?

The area function is f(x) = −(x − 3)² + 9, which is in vertex form. Since the squared term has a negative coefficient, the parabola opens downward, so its vertex gives the maximum. The vertex has area 9, so the maximum area is 9 square units (choice B).

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