The document defines quadratic equations as polynomial equations of the second degree where the highest exponent is 2. It provides the general form of a quadratic equation as ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. There are three main ways to solve quadratic equations: factoring, completing the square, and using the quadratic formula. Factoring involves finding two linear expressions whose product is the quadratic, while completing the square rewrites the equation in the form of a perfect square trinomial. The discriminant, b2 - 4ac, determines the nature of the roots.