Quadratic equations are often used to describe the motion of objects that fly through the air. Quadratic equations can be applied to problems in physics involving parabolic motion, path, shape, and stability.
Engineers of all sorts use these equations. They are necessary for the design of any piece of equipment that is curved, such as auto bodies,aeroplane,ship etc.
Astronomers use quadratic equations to describe the orbits of planets, solar systems and galaxies. Physicists use them to describe different types of motion.
In business For example, figuring out how to design and pay for pension plans involves quadratic equations. As insurance plans are based on models that often involve these types of equations.