The quasi-linear quadratic utility model is widely used in economics. The knowledge of its exact origin is less widespread. A first contribution of the paper is to explain the genesis of this model. Next, we review the main properties of the general model, mainly following the previous literature. Finally, it is shown that all the tractable versions of the model used in practice are (almost) identical and have a mean variance structure. We provide ready-to-use formulae for this symmetric model.