I want to prove that $f(x) = -\lVert x \rVert^2$ is not convex.

I know that $f(x) = \lVert x \rVert^2$ is convex by the following proof:

\begin{equation} \label{eq1}
\begin{split}
\lVert \alpha x + (1 - \alpha )y \rVert^2 & \leq \lVert \alpha x\rVert^2 + \lVert (1 - \alpha)y\rVert^2 \\
 & = \alpha^2\lVert x\rVert^2 + (1 - \alpha)^2\lVert y\rVert^2 \\ & \leq \alpha \lVert x\rVert^2 + (1 - \alpha) \lVert y\rVert^2
\end{split}
\end{equation}

How do I prove that the negative version of this is not convex? Intuitively I know that it must be concave, but I don't know how I can prove.