In the class of mappings \(f: X\to Y\) between commutative groups \(X,Y\) (the latter without elements of order two) the functional equations \[ f(2x+y)=4f(x)+f(y)+f(x+y)-f(x-y),\eqno{(1)} \] \[ f(2x+y)+f(2x-y)=8f(x)+2f(y)\eqno{(2)} \] and the classic \textit{quadratic functional equation} \[ f(x+y)+f(x-y)=2f(x)+2f(y)\eqno{(3)} \] are equivalent. The main results of the paper consider the stability of (1) and (2). Let \(Y\) be a real Banach space and suppose that \[ \|f(2x+y)-4f(x)-f(y)-f(x+y)+f(x-y)\|\leq\varphi(x,y) \] or \[ \|f(2x+y)+f(2x-y)-8f(x)-2f(y)\|\leq\varphi(x,y) \] for some control mapping \(\varphi: X\times X\to [0,\infty)\). Then \(f\) can be approximated by a quadratic mapping and the error of the estimation is expressed by \(\varphi\). The results generalize earlier ones obtained by \textit{J.-R. Lee, C. Park} and \textit{J. Su An} [Abstr. Appl. Anal. 2008, Article ID 628178, 8 p. (2008; Zbl 1146.39045)]. In the paper under review, both the setting and the form of the control mapping \(\varphi\) are more general.