Show that $f(x+\alpha h) - f(x) = 1/2(H(x)\alpha h, \alpha h) + o(\alpha^2), h \in \mathbb{R}^n, \alpha > 0$ where $H(x)$ is the hessian of $f(x)$

Question

Show that $f(x+\alpha h) - f(x) = 1/2(H(x)\alpha h, \alpha h) + o(\alpha^2), h \in \mathbb{R}^n, \alpha > 0$ where $H(x)$ is the hessian of $f(x)$. Edit: also $\nabla f(x) = 0$. I can show that $f(x+\alpha h) - f(x) = (\nabla f(x), \alpha h) + o(\alpha)$. But I'm not sure where to go from here. Any hints?