In this work we give a detailed look to the Practical implementation of unconstrained optimization tested on quadratic functions. Section (1) speak about the theory of optimization problems, introduce definitions and theorems of linear programming problems , definitions and theorems of quadratic programming problems . Section (2) introduce some methods of unconstrained optimization. In section(3) we look at methods for approximating solutions to equations, solving unconstrained optimization problems . Section(4) gives practical implementation of some method s using Matlab programs
