How are quadratic equations used in the real world?
An equation that describes motion is often quadratic, as are equations that describe the shape of things like satellite dishes (parabolic reflectors) and lenses. One example can be seen on suspension bridges. The main cables are in the shape of a parabola and the formula for them is quadratic. Galileo described the trajectory of cannon balls as quadratic, with the maximum range being 1/16 times v2 (where v is the speed at which the cannon ball comes out of the cannon. Until his analysis, artillerymen didn’t know exactly how their cannon balls flew, and aiming was a best-guess estimate. Even today artillery shots are calculated with the science of ballistics and use the same equations of motion. They also calculate other variables, like the drag an object feels when it travels through the air, how wind and air density affect a trajectory and other factors – but the underlying equations of motion haven’t changed. A basic problem with quadratic equations. When polynomials are multiplied t
