Question

write a quadratic function in standard form that represents each area as a function of the width. remember to define your variables. a builder is designing a rectangular parking lot. she has 300 feet of fencing to enclose the parking lot around three sides.​

Answer 1

Check Explanation

Explanation:

Let the width of the parking lot be x ft

The length of the parking lot be y ft

And let us first assume that the rectangular parking lot is enclosing about the dimension of a length of the parking lot.

That is, (y + x + x) = 300

(y + 2x) = 300

Area of the parking lot = A(x, y) = xy

But from the constraint equation,

y = 300 - 2x

Substituting for y in the Area equation

A(x) = x(300 - 2x) = (300x - 2x²)

A(x) = -2x² + 300x

If we now assume that the rectangular parking lot is enclosing the width side of the parking lot,

(x + y + y) = 300

(x + 2y) = 300

2y = (300 - x)

y = (300 - x)/2

y = 150 - (x/2)

A(x,y) = xy

Substituting for y again

A(x) = x[150 - (x/2)]

A(x) = 150x - (x²/2)

A(x) = (-x²/2) + 150x

So, depending on which side of the rectangle the parking lot is enclosing and which 3 sides make up the 300 ft constraint, the Area can be given in the two forms presented above.

Hope this Helps!!!