\documentclass[tikz]{standalone}

\usepackage{pgfplots}

\pgfplotsset{compat=1.14}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[xmin=-5, xmax=5, width=12cm, height=5cm, xlabel={$z$}, ylabel={$E_p$}, ytick={0}, xtick={0}]
        \addplot  [domain=-5:5, mark=none, samples=30, smooth] {1/2 * (x^4/2 - 8 * x^2)};
    \end{axis}
\end{tikzpicture}

\end{document}
