A quadratic is a type of polynomial that has the general form ax^2 + bx + c , where a , b , and c are constants, and a is not zero. The highest exponent in a quadratic equation is 2, which means it can be represented graphically as a parabola. Quadratics can have various shapes depending on the value of a ; if a is positive, the parabola opens upwards, and if negative, it opens downwards. Quadratic equations can be solved using several methods, including factoring, completing the square, or applying the quadratic formula: x = \frac-b \pm \sqrt{b^2 - 4ac}2a . The solutions to a quadratic equation are known as the roots, which can be real or complex numbers. Quadratics are widely used in various fields, including physics, engineering, and economics, to model different types