\bigskip

\exercice[style=A,N=1]{Forme canonique et lecture graphique}

Associer les 4 fonctions suivantes à leur représentation graphique ci-dessous.

\begin{multicols}{2}
$f(x)=-2(x+1)^2+3$

$g(x)=(x-1)^2-3$

$h(x)=2(x+3)^2-1$

$j(x)=-\dfrac{1}{2}(x-3)^2+1$
\end{multicols}

\begin{center}
\begin{tikzpicture}[>=latex]
\draw[thick,->] (-5,0) -- (5,0);
\draw[thick,->] (0,-5) -- (0,5);
\foreach\x in {-4,-3,-2,-1,1,2,3,4}
{
	\draw[thick] (\x,0.1) -- (\x,-0.1) node[below] {$\x$};
	\draw[thick] (0.1,\x) -- (-0.1,\x) node[left] {$\x$};
}
\node[below left] at (0,0) {0};
\clip (-5,-5) rectangle (5,5);
\draw[thick,purple] plot[domain=-5:5,samples=100] (\x,{-2*(\x+1)^2+3});
\draw[thick,violet] plot[domain=-5:5,samples=100] (\x,{(\x-1)^2-3});
\draw[thick,blue] plot[domain=-5:5,samples=100] (\x,{2*(\x+3)^2-1});
\draw[thick,red] plot[domain=-5:5,samples=100] (\x,{-0.5*(\x-3)^2+1});
\node[blue,right] at (-1,4) {${\cal C}_1$};
\node[red,right] at (-1,-4.5) {${\cal C}_2$};
\node[right,violet] at (4,4) {${\cal C}_3$};
\node[purple] at (-3.5,-4) {${\cal C}_4$};
\end{tikzpicture}
\end{center}