Question

Simon has a certain length of fencing to enclose a rectangular area. The function A models the rectangle's area (in square meters) as a function of its width (in meters).

Answer 1

When there is no width the area is 0m^2

Explanation:

I took the quiz.

Answer 2

The maximum area is 1,600 square meters

Explanation:

The complete question is

What is the maximum area possible?

The given function area is modeled by A(w)=-w(w-80)

we know that

The given function is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex represent the width for the maximum area

The y-coordinate of the vertex represent the maximum area

Convert the quadratic function in vertex form

`A(w)=-w(w-80)\\\\A(w)=-w^(2)+80w`

Factor -1

`A(w)=-(w^(2)-80w)`

Complete the square

`A(w)=-(w^(2)-80w+1,600)+1,600`

Rewrite as perfect squares

`A(w)=-(w-40)^(2)+1,600` ----> function in vertex form

The vertex is the point (40,1,600)

therefore

The maximum area is 1,600 square meters