In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{sigma}(y))+f(y+{sigma}(z))+f(x+{sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${eta}$-normed space and ${sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{sigma}(y))+f(y+{sigma}(z))+f(x+{sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.