The function f(x) = –(x – 3)2 + 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 function is in vertex form: f(x) = −(x − 3)² + 9. Since the squared term is multiplied by a negative number, the parabola opens downward, so its vertex gives the maximum value. The vertex’s y-coordinate is 9, so the maximum area is 9 square units (choice C).

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