\begin{tikzpicture}
[+preamble]
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{patterns}
[/preamble]
\begin{axis}[
axis equal,
grid,
grid style={dashed,gray!30},
smooth,
xmin=-2, xmax=2,
ymin=-1.5, ymax=3.5,
axis lines=middle,
xlabel=$x$,
xlabel style={below, anchor=north east,inner xsep=0pt},
xtick={-2,…,2},
ylabel=$y$,
ylabel style={above,anchor=north east,inner ysep=0pt},
ytick={-1,…,3},
samples=100,
legend style={at={(1,1)},xshift=0cm,anchor=north east,nodes=right,fill=none}
]
\addplot[red,name path=f1,mark=none,domain=-2:2,line legend,thick] {3-x^2};
\addlegendentry{$f_{1}(x)$}
\addplot[blue,name path=f2,mark=none,domain=-1.4:1.4, line legend,thick] {3*x^2-1};
\addlegendentry{$f_{2}(x)$}
\path[name path=lower,intersection segments={of=f1 and f2,sequence=B0 –A1}];
\addplot[pattern=north west lines, pattern color=green]fill between[of=f2 and lower];
\addlegendentry{$\cal{A}$}
\end{axis}
\end{tikzpicture}