% TeX root = ../main.tex

\begin{tikzpicture}[scale=0.5]
    \begin{axis}[
        axis lines = center,
        axis on top,
        xmin=-3.3,
        xmax=3.3,
        ymin=-3.3,
        ymax=3.3,
        y=1cm,
        x=1cm,
        ytick={-3,...,3},
        xtick={-3,...,3},
        xlabel = x,
        ylabel = y,
        font=\tiny
    ]
        \addplot [
            % domain={-1.65:3},
            name path = B,
            thick,
            % pattern=north east lines,
        ] {0.5*x*x-2};
        \addplot[name path=D,draw=none] {-3.3};

        \addplot[pattern=north east lines,pattern color=red!30] fill between[of=B and D];
        \addplot[only marks,mark=o] coordinates {
            (-3,  3) (-2,  3) (-1,  3) (0,  3) (1,  3) (2,  3) (3,  3)
                     (-2,  2) (-1,  2) (0,  2) (1,  2) (2,  2)        
                     (-2,  1) (-1,  1) (0,  1) (1,  1) (2,  1)        
                     (-2,  1) (-1,  1) (0,  1) (1,  1) (2,  1)        
                              (-1,  0) (0,  0) (1,  0)                
                              (-1, -1) (0, -1) (1, -1)                
        };
    \end{axis} 
\end{tikzpicture}