# Pre-Calc help needed: Quadratic Functions

• November 12th 2006, 06:59 PM
paul
These questions are part of a project I am working on for my class. Below is the problem situation. I've been trying to figure this out for hours:

Problem: Maximum Storage Area

A company wants to build an area to store machinery. One side (a length side) borders a river, so fencing will be needed for the other three sides. The company has 528 ft. of chain-link fencing. Assume that the company wishes to use all of the fencing and the "width" refers to the measure of the two sides that are perp. to the river and "length" refers to the side parl. to the river.

Table:
W: 25 50 75 100 125 150 175 200
L : 478 428 378 328 278 228 178 128
A: 11950 21400 28350 32800 34750 34200 31150 25600

Questions I need help with:

1) Let W represent the width. Express the length in terms of W.

2) Write the general formula for the area of a rectangle (I know this one, but it ties into the next question). A = L x W

3) Using the general formula in (2), write the area (A) of the enclosure as a function of W.

Thank you, in advance, for help with this.

*edit: the numbers in the table are a little messed up, sorry.
• November 12th 2006, 07:20 PM
Quick
Quote:

Originally Posted by paul
These questions are part of a project I am working on for my class. Below is the problem situation. I've been trying to figure this out for hours:

Problem: Maximum Storage Area

A company wants to build an area to store machinery. One side (a length side) borders a river, so fencing will be needed for the other three sides. The company has 528 ft. of chain-link fencing. Assume that the company wishes to use all of the fencing and the "width" refers to the measure of the two sides that are perp. to the river and "length" refers to the side parl. to the river.

Table:
W: 25 50 75 100 125 150 175 200
L : 478 428 378 328 278 228 178 128
A: 11950 21400 28350 32800 34750 34200 31150 25600

Questions I need help with:

1) Let W represent the width. Express the length in terms of W.

You know that: $2w+l=528$

Thus: $l=528-2w$

Quote:

2) Write the general formula for the area of a rectangle (I know this one, but it ties into the next question). A = L x W

3) Using the general formula in (2), write the area (A) of the enclosure as a function of W.
You have $A = wl$

Substitute: $A=w(528-2w)$

Thus: $A=528w-2w^2$

Switch into standard notation: $\boxed{A=-2w^2+528w}$