Paraboloid in LaTeX with TikZ

\documentclass[border=5mm]{standalone}

\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}[scale=1,yscale=.5]

\draw (0,0) arc (180:0:2);
\draw ({2-sqrt(3)},1) arc (180:0:{sqrt(3)});
\draw ({2-sqrt(2)},2) arc (180:0:{sqrt(2)});
\draw (1,3) arc (180:0:1);

\draw (0,0) arc (-180:0:2);
\draw ({2-sqrt(3)},1) arc (-180:0:{sqrt(3)});
\draw ({2-sqrt(2)},2) arc (-180:0:{sqrt(2)});
\draw (1,3) arc (-180:0:1);

\draw (0,0) parabola bend (2,4) (4,0);
\draw ({2-sqrt(2)},{-sqrt(2)}) parabola bend (2,4) ({2+sqrt(2)},{sqrt(2)});
\draw ({2-sqrt(2)},{-sqrt(2)}) parabola bend (2,4) ({2+sqrt(2)},{sqrt(2)});

\draw ({2-sqrt(2)},{-sqrt(2)}) node [below] {0};
\draw [->]({2-sqrt(2)},{-sqrt(2)}) --++ (5,5);
\draw ({2-sqrt(2)},{-sqrt(2)}) --++ (-2,-2);
\draw [->]({2-sqrt(2)},{-sqrt(2)}) --++ (-3,3);
\draw ({2-sqrt(2)},{-sqrt(2)}) --++ (3,-3);

\end{tikzpicture}

\end{document}