# Everyday Examples of Situations to Apply Quadratic Equations

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Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0. The letter X represents an unknown, and a b and c being the coefficients representing known numbers and the letter a is not equal to zero.

## Calculating Room Areas

People frequently need to calculate the area of 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. For example, if you have only 4 square feet of wood to use for the bottom of the box, with this information, you can 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 times 2x, or 2x^2. This equation must be less than or equal to four to successfully make a box using these constraints.

## Figuring a Profit

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 items 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 per glass, you're not likely to sell any, but at$0.01 per 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. You've estimated 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 times 12 minus 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.