Code comment for https://tex.stackexchange.com/questions/407148/

pgfplotsdemoplot.tex

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
      xlabel=$x$,ylabel=$y$,
      xtick={100},ytick={100},
      no marks,axis equal,axis lines=middle,
      xmin=-9,xmax=8,ymin=-8,ymax=8,
      enlargelimits={upper=0.1},
      samples=51,
      every axis plot/.append style={
         every node/.style={font=\scriptsize}
      }
    ]

    \addplot [domain=-6:6, variable=t] ( {sqrt(t^2+4)/sqrt(2)}, {t} )
          node[below,pos=0]{$x=\sqrt{y^2+4)/2}$};
    \addplot [domain=-6:6, variable=t] ( {-sqrt(t^2+4)/sqrt(2)}, {t} )
          node[below,pos=0]{$x=-\sqrt{y^2+4)/2}$};

    \addplot [domain=-4:4, variable=t] ( {t^2/2}, {t} )
          node[above]{$y^2=2x$};

    \addplot [samples=2, domain=-7:7] {0} node[very near end,below] {$y=0$};
    \addplot [samples=2, domain=-7:7] {1} node[very near end,above] {$y=1$};

    \node[below left,font=\scriptsize] at (0,0) {$O$};
    \node[above left,font=\scriptsize] at (0,1) {$1$};

\end{axis}
\end{tikzpicture}
\end{document}