A quadratic surface is a three-dimensional geometric shape defined by a second-degree polynomial equation in three variables, typically represented as Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0 . Common examples of quadratic surfaces include ellipsoids, hyperboloids, and paraboloids, each characterized by specific coefficients and terms in their equations. These surfaces can be visualized as the three-dimensional analogs of conic sections, which are curves formed by the intersection of a plane and a cone. Quadratic surfaces are important in various fields, including mathematics, physics, and engineering, as they model real-world phenomena and structures.