A functional equation originating from quadratic forms ✩

In this paper, we obtain the general solution and the stability of the 2-variable quadratic functional equation f (x +y, z +w) +f (x − y, z − w) = 2f (x,z) +2f (y,w). The quadratic form f (x, y) = ax2 +bxy +cy2 is a solution of the above functional equation. © 2006 Elsevier Inc. All rights reserved.