A procedure to approximate the non-dominated set for general (continuous) bi-criteria programs is proposed. The piecewise approximation is composed of quadratic curves, each of which is developed locally in a neighbourhood of a non-dominated point of interest and based on primal-dual relationships associated with the weighted Tchebycheff scalarization of the original problem. The approximating quadratic functions, in which decision maker's preferences are represented, give a closed-form description of the non-dominated set. A numerical example is included.