\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 [
name path = B,
thick,
] {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}