The qualitative features of the phase portraits of the class of quadratic systems given by
is studied. For example, it is shown that if such a system has at most two critical points at infinity, then either it has a center or it has at most one periodic orbit. If there is a unique periodic orbit it is a hyperbolic limit cycle. A nice application of the theory developed in the paper is made to a quadratic system which arises in the study of shear flow of a non-Newtonian fluid.