In the Real World
A quadratic equation can be used to describe the arc that a ball travels in the air, with x being the distance it moves and y its height. You can also relate the ball's height, y, to the amount of time it has been in the air, x. And it doesn't have to be a ball—it could be a spherical cow, or a chunk of frictionless ice, or a pendulum with a massless spring that experiences no air resistance.
Quadratic equations also have a practical application in statistics. As we mentioned when talking about linear regression, sometimes the dots in a scatter plot end up looking like a line, while other times they look like a curve. Just as we can use linear regression to fit a line to the dots, there are various forms of non-linear regression that can fit different curves. Quadratic regression is one of the more common types of non-linear regression.