in this paper, we solve the quadratic $alpha$ -functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f( alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.
