What is the quadratic equation and what does it do?
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Let’s try a simpler explanation and start at a little more basic point.
When two things are related, you can express their relation using an equation. The type of equation tells us how they are related. For example, how much money you spend when you buy 1 item vs. 10 items is linear. Just multiply both the cost and the item count by 10 and you get the answer. How far can you travel at a constant speed in one hour vs. 2 hours? All of these are called linear relationships.
Some relationships are a little more complex. For example, what if the speed itself changes? If you apply constant acceleration continuously for an hour, the speed increases, because speed is linearly related to acceleration. The distance is now linearly related to something that is itself linearly increasing. This makes the distance related to the square of time. This is now called a quadratic equation. That is all that defines a quadratic equation – the unknown quantity changes based on the square of the known quantity. You can have a linear component and a constant component added, but as long as there is a square component and nothing higher (third power, etc.) it will be a quadratic equation.
The quadratic equation is useful because it describes how these quantities change and help predict them. There are a lot of these relationships found in nature and mathematics. A lot of motion is based on solving quadratic equations, so it helps us plan and predict everything from missiles and space launches to calculating square footage in a home.
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