In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of function evaluations have been reduced obviously through our algorithms.