Quadratic surfaces are three-dimensional shapes defined by second-degree polynomial equations in three variables. These surfaces can take various forms, including ellipsoids, hyperboloids, and paraboloids, depending on the coefficients and terms in the equation. They are important in fields like geometry, physics, and engineering, as they help model real-world phenomena. The general equation of a quadratic surface can be expressed as Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0. Each type of surface has unique properties and applications, making them essential for understanding spatial relationships in mathematics and science.