This paper presents the following research works. First, numerical simulation is applied to verify the quadratic pattern of system status such as generator dispatches and line flows with respect to load changes. Second, an algorithm based on quadratic interpolation is proposed to reduce the intensive computation with brute-force simulation approach in calculating the coefficients of the quadratic pattern. Third, a heuristic algorithm to seek three load levels for the quadratic interpolation is proposed. This heuristic algorithm employs the DCOPF-based congestion prediction algorithm to estimate critical load levels. Fourth, the congestion prediction algorithm is presented using the quadratic properties of marginal unit generation and line flow. Last, the proposed algorithms are tested on the PJM 5-bus system, and results demonstrate the high effectiveness and high accuracy of the proposed approach.