Notes

People frequently need to calculate the area of things like rooms, boxes or plots of land. An example might involve building a rectangular box where one side must be twice the length of the other side. So long as this ratio is satisfied, the box will be as a person wants it. Say, however, that a person has only 4 square feet of wood to use for the bottom of the box. Knowing this, the person needs to create an equation for the area of the box using the ratio of the two sides. This means the area -- the length times the width -- in terms of x would equal x(2x), or 2x^2. This equation must be less than or equal to 4 for the person to successfully make a box using his constraints. Once solved, he now knows that one side of the box must be sqrt(2) feet long, and the other must be 2[sqrt(2)] feet long (adopted from Reference 1).

Sometimes calculating a business' profit requires using a quadratic function. If you want to sell something -- even something as simple as lemonade -- you need to decide how many things to produce so that you'll make a profit. Let's say, for example, that you're selling glasses of lemonade, and you want to make 12 glasses. You know, however, that you'll sell a different number of glasses depending on how you set your price. At $100/glass, you're not likely to sell any, but at $0.01/glass, you'll probably sell 12 glasses in less than a minute. So, to decide where to set your price, use P as a variable. Let's say you estimate the demand for glasses of lemonade to be at 12 - P. Your revenue, therefore, will be the price times the number of glasses sold: P(12 - P), or 12P - P^2. Using however much your lemonade costs to produce, you can set this equation equal to that amount and choose a price from there (adopted from Reference 2)