A quadratic is a type of polynomial that has the general form of ax^2 + bx + c , where a , b , and c are constants, and x represents a variable. The highest exponent in a quadratic equation is 2, which gives it a parabolic shape when graphed. Quadratics can have zero, one, or two real solutions, depending on the value of the discriminant b^2 - 4ac . Quadratic equations are commonly encountered in various fields, including physics, engineering, and finance. They can model a range of real-world situations, such as projectile motion and profit maximization. The solutions to quadratics can be found using methods like factoring, completing the square, or applying the quadratic formula, which is x = \frac-b \pm \sqrt{b^2 - 4ac}2a .