The most common use of the quadratic equation in real world situations is in the aiming of missiles and other artillery by military forces. Parabolas are also used in business, engineering and physics.
The parabola is key in determining where something lands when thrown, shot or launched. By factoring in the height the object is predicted to reach and the velocity with which it is projected, and accounting for gravity, it is possible to determine fairly accurately where the projectile is likely to land. The military uses the quadratic formula all the time to determine where artillery is likely to fall and to target flying objects.
Engineers use the quadratic equation along with other advanced types of math when making their designs. The only way they can assure that a curved object is made perfectly is by using the quadratic formula to shape the object as a parabola. Automotive, chemical, electrical and even audio engineers all use this method.
The quadratic equation also has important applications in business. When product developers create a new item to sell, they use the quadratic formula to create a demand curve and use it to determine the optimal price to sell the units to maximize profits.