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?

Answer 1

C. 9

Explanation:

EDG2020

Answer 2

Maximum area = 9 sq units

Explanation:

`f(x)=-(x-3)^2+9`

which represents the area . As it is a quadratic equation it represents the parabola . And the vertex of the parabola will maximum area of for some value of x

let f(x) = y

`y=-(x-3)^2+9`

`(x-3)^2=-(y-9)`

Comparing it with the standard equation of parabola

`y=(x-h)^2+k`

we get h=3 and y=9

where (h,k) is the vertex (3,9)

Hence the maximum area of the rectangle will be 9