Asap martha is fencing off a small herb garden in her backyard. if she has 20 feet of fencing and wants a rectangular garden, what length and width will give her the largest area? draw the graph of the function a(w) for area in terms of width and determine the maximum.

The maximum area is for a square garden with length side of

Step-by-step explanation:

Let

L-----> the length o the rectangular garden

W ---> the width of the rectangular garden

we know that

The perimeter is equal to

so

-----> equation A

The area of the rectangular garden is equal to

----> equation B

substitute equation A in equation B

This 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 of the rectangular garden

using a graphing tool

The vertex is the point (5,25)

see the attached figure

therefore

The maximum area is

The width is

Find the value of L

The length is the same that the width

so

The maximum area is for a square garden with length side of

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )