In this paper, a quadrex algorithm for quadratic programming problems is introduced (n = 2) under linear and quadratic constraints. The quadrex algorithm considers on the behavior of the quadratic function near the origin or a translate of the origin, performs a series of translationsand orthogonal rotations to obtain the optimal solution of the objective function as well as taking considerations on the constraints of the problem. The method works provided that the eigenvalues of the matrix on quadratic form of the objective function is strictly negative, that is,Q is negative-definite. The quadrex algorithm is a parallel counterpart of the simplex algorithm for linear programming models.