Solving area of a 3 sided rectangular corral?

[emg1102]

I'm trying to figure out how to solve the following problem:

A 120 m trapping net stretched out into a 3 sided rectangular corral is used to front a flowing river.

What value of widths (w), being parallel to the riverbanks, will provide the corral with the largest capturing area.

Choices:

A. w = 15 m
B. w = 20 m
C. w = 25 m
D. w = 30 m
E. w = 35 m

The correct answer is D.

 

[pka]

2W+L=120 & A=WL=W(120-2W)
Area A=120W-2W<SUP>2</SUP> is a parabola opening dpwn.
The maximum area is at the vertex.
Can you find the vertex?

 

[emg1102]

Capturing Area - Help

2W+L=120 & A=WL=W(120-2W)
Area A=120W-2W<SUP>2</SUP> is a parabola opening dpwn.
The maximum area is at the vertex.
Can you find the vertex?

I think to find the vertex I need the zeroes of the equation, but since It's not factored, I am unsure about how to go about finding it.

Also, How can I tell that it is a parabola opening down?

Thank you for your help - I'm a little rusty.

 

[pka]

Why not graph the function?
You will see!