In secondary schools students learn to investigate the behavior of the quadratic function in one variable, and to find the point where the function reaches its extremal value. The purpose of this article is to demonstrate how the idea which is applied to functions in one variable can be extended and applied to functions in several variables. We present the procedure to determine whether a quadratic function in several variables has a minimum or a maximum, and if it has, to find points in which the extremal value is reached. This procedure leads to several theoretical results.