Problem with a TikZ/Geogebra plot of an exponential function (even if using CVS version definition)

I wanted to graph the function f(x)=(-1+4x^2)*e^2 in a coordinate system. Using "Export Graphics View as pgf/TikZ" in Geogebra I got the following code (here shown after I did some minor changes regarding color and arrow style).

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
[scale=2,line cap=round,line join=round,x=1.0cm,y=1.0cm]
\draw [color=black!70,dash pattern=on 1pt off 1pt, xstep=0.5cm,ystep=0.5cm] (-1.45,-1.28) grid (1.45,2.48);
\draw[->,line width=1,color=black] (-1.45,0) -- (1.45,0);
\foreach \x in {-1,1}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
\draw[color=black] (1.31,0.04) node [anchor=south west] { x};
\draw[->,line width=1,color=black] (0,-1.28) -- (0,2.48);
\foreach \y in {-1,1,2}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
\draw[color=black] (0.05,2.28) node [anchor=west] { y};
\clip(-1.45,-1.28) rectangle (1.45,2.48);
\draw[line width=1,color=black!80,fill=black!80,fill opacity=0.6, smooth,samples=50,domain=0.0:0.5] plot(\x,{(4*\x^2-1)*2.7183^\x}) -- (0.5,0) -- (0,0) -- cycle;
\draw[line width=1,smooth,samples=100,domain=-1.5:1.5] plot(\x,{(-1+4*\x^2)*2.7183^\x});
\end{tikzpicture}
\end{document}


The code above gave me this result:

I tried installing TikZ CSV from this page following steps given here but this only flooded the log in "Undefined control sequence" messages.

Instead I tried using Jake's answer code to improve the exp-function. Then the result looked a bit better but still not correct:

Here is how the original graph is shown in Geogebra (Wolfram Alpha shows similar results):

Obviously the exp-code is not helping enough, so maybe there still is a bug in that? Can someone help me with this? Would it be possible to plot the graph correctly in some other way? If so, what would that code look like?

-
Welcome to the site! – cmhughes Oct 14 '13 at 18:37
It seems the problem is the x^2 (which I'm sure was addressed ages ago). Using -1+4*(\x)^2))*2.7813^\x appears to work. – Mark Wibrow Oct 14 '13 at 18:46
Just to add to my previous comment, with TikZ plots each y-value is expanded for every value of \x so you get (-1+4*-1.5^2)*2.7183^-1.5 which is then evaluated as -2.23 (this result is the same as python and matlab). This means the \x^2 must be given as (\x)^2. PGFPlots (like numpy and matlab) does extra stuff to ensure that when x is (effectively) a vector then x^2 is equivalent to (x)^2. – Mark Wibrow Oct 15 '13 at 7:12
Thank you very much! This both explained why the results were not correct (Marks answer) and how it could be done way better with pgfplots (cmhughes answer) – Bea Oct 16 '13 at 16:43

GeoGebra is a wonderful tool for creating interactive tools for students, and while the code it produces using its export feature is pretty impressive, it can usually not beat a hand-made solution, especially for readability and cleanness.

Here's a hand-made solution using pgfplots

% arara: pdflatex
% !arara: indent: {overwrite: true, trace: on}
\documentclass{standalone}

\usepackage{pgfplots}

% axis style
\pgfplotsset{every axis/.append style={
axis x line=middle,
axis y line=middle,
axis line style={<->},
xlabel={$x$},
ylabel={$y$},
},
framed/.style={axis background/.style ={draw=black}},
}

% arrow style
\tikzset{>=stealth}

\begin{document}

\begin{tikzpicture}
\begin{axis}[framed,
xmin=-5,xmax=5,
ymin=-5,ymax=5,
minor xtick={-3,-1,...,3},
minor ytick={-3,-1,...,3},
grid=both
]