Question

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?
3 square units
6 square units
9 square units
12 square units

Explanation:

Step1: Analyze the function form

The function $f(x)=-(x - 3)^2+9$ is in vertex - form $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. Here $a=-1$, $h = 3$, $k = 9$.

Step2: Determine the maximum value

Since $a=-1<0$, the parabola opens downwards. The vertex of a parabola that opens downwards represents the maximum point of the function. The $y$-coordinate of the vertex gives the maximum value of the function.

Answer:

C. 9 square units