

\documentclass[a4paper,12pt,twoside]{article}
\usepackage[utf8x]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\usepackage{amsmath,amssymb}

% package TikZ
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\usetikzlibrary{arrows.meta,arrows}


\begin{document}

% TikZ
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\definecolor{qqwuqq}{rgb}{0.,0.392156862745,0.}
\definecolor{cqcqcq}{rgb}{0.752941176471,0.752941176471,0.752941176471}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\draw [color=cqcqcq,dash pattern=on 4pt off 4pt, xstep=2.0cm,ystep=2.0cm] (-6.58888315222,-5.18344029733) grid (6.9548138587,12.2678219576);
\draw[->,color=black] (-6.58888315222,0.) -- (6.9548138587,0.);
\foreach \x in {-6.,-4.,-2.,2.,4.,6.}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
\draw[->,color=black] (0.,-5.18344029733) -- (0.,12.2678219576);
\foreach \y in {-4.,-2.,2.,4.,6.,8.,10.,12.}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};
\clip(-6.58888315222,-5.18344029733) rectangle (6.9548138587,12.2678219576);
\draw[color=qqwuqq,smooth,samples=100,domain=-6.588883152215031:6.954813858702505] plot(\x,{(\x)^(2.0)+2.0*(\x)-4.0});
\draw (2.13674797527,3.61806588344) node[anchor=north west] {Démonstration};
\draw[color=ffttww,smooth,samples=100,domain=-6.588883152215031:6.954813858702505] plot(\x,{2.718281828^(-(\x)^(2.0)+2.0)});
\begin{scriptsize}
\draw[color=qqwuqq] (-4.65406929351,12.1919469044) node {$f$};
\draw[color=ffttww] (-17.0217029786,-0.251561833969) node {$g$};
\end{scriptsize}
\end{tikzpicture}
%----
%----
\end{document}