The existence of a canonical form for quadratic linearization of a linearly controllable system has been shown. However, if a linearly controllable system is amenable to quadratic linearization, it is not clear how to derive the transformation leading to quadratic linearization. Our approach to the derivation of necessary and sufficient conditions for quadratic linearization is constructive in nature in the sense that once the conditions are satisfied, the normalizing and input transformations are derived leading to quadratic linearization. We use state feedback to make the system eigenvalues non-resonant allowing the closed-form solution of the generalized homological equations which leads to the transformation solution. The proposed technique is illustrated with an example.