Let Xbe a normed space, Ybe a Banach space and f,g:X→Y. In this paper, we investigate the Hyers–Ulam stability theorem for the generalized quadratic functional equation f(kx+y)+f(kx-y)=2k2g(x)+2f(y)in a set Ω⊂X×X, where kis a positive integer. By the Baire category theorem, we derive some consequences of our main result.