a relation between an input and an output

A farmer purchased 800 feet of fencing to fence a rectangular area along a straight river. He needs no fencing along the river side.
• Sketch a diagram that represent this situation and label the sides of the rectangle by L for the length and W for the width. (Remember no fence is used along the river).
• Write an equation that relates the sides L and W of the rectangle to 800 the fencing purchased.
• Write an equation that relates the area A of the rectangle to L and W.
• Use the equation you wrote in question 2) to isolate L by itself.
• Use the value of L from question 4) to replace L in question 3)
• a) Simplify the equation resulting in question 5)
b) Identify the two variables that are changing with each other.
c) Identify the dependent variable and the independent variable. 
 d) Identify what kind of function is this. 
 e) What graph will model this function and how does it open?
 f) Identify the vertex and find its coordinates.
 g) What does the vertex tell us?
h) What are the dimensions L and W that produced the maximum area A?

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