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

Answer:

The maximum area is 1,600 square meters

Step-by-step 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

Answer 2

Answer:

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

Step-by-step explanation:

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