A quadratic equation is a type of polynomial equation that can be expressed in the standard form ax^2 + bx + c = 0 , where a , b , and c are constants, and a is not zero. The variable x represents an unknown value. Quadratic equations are characterized by their highest exponent being 2, which gives them a parabolic shape when graphed. Solutions to a quadratic equation can be found using various methods, including factoring, completing the square, or applying the quadratic formula, which is x = \frac-b \pm \sqrt{b^2 - 4ac}2a . The solutions, known as roots, can be real or complex numbers, depending on the value of the discriminant b^2 - 4ac .