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

Answer 1

Answer:

Maximum area = 9 sq units

Step-by-step 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