Prove or disprove that the function is convex

Employing the SimpliFired version of the problem gives the following pictorial comment.
Scale in $y$-direction is $10$ times the one in $x$-direction.

Ipse est: $\,\sum\limits_{k=2}^{2n}(k^4-k^2)(-x)^{k^2-4}\ge0\,$ for $\,n\ge 1\,$ and $\,0\le x \le 1\,$.
Or does it count as a proof without words?