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\begin{document}%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 14116811957822--
%%--Etude graphique d\'une fonction et résolutions d\'équations--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%


\begin{exercise}
On consid\`{e}re la fonction $f$ d\'{e}finie sur l'intervalle $[-3;5]$ par:
\[
f(x)=x^{2}-2x+1
\]
On donne sa repr\'{e}sentation graphique sur la figure \ref{0512002029} de la
page \pageref{0512002029}.

\begin{enumerate}
\item Par lecture graphique, dresser le tableau de variation de la fonction
$f$.

\item
\begin{enumerate}
\item Par lecture graphique, donner le \textbf{minimum} de la fonction $f$ et
pr\'{e}ciser pour quelle valeur il est atteint.

\item Par lecture graphique, donner le \textbf{maximum} de la fonction $f$ et
pr\'{e}ciser pour quelle valeur il est atteint.

\item Par lecture graphique, donner les images de $0$ et de $4$ par $f$; puis
les ant\'{e}c\'{e}dents \'{e}ventuels par $f$ de $4$ et de $-2$.

\item Par la m\'{e}thode de votre choix, d\'{e}terminer $f(-1)$.

\item R\'{e}soudre dans $[-3;5]$ l'\'{e}quation $f(x)=9$.
\end{enumerate}

\item Tracer sur la figure \ref{0512002029} de la page \pageref{0512002029},
les droites $D_{1}$ et $D_{2}$ d'\'{e}quation:
\[
D_{1}:\,y=-2x+3\qquad\text{et}\qquad D_{2}:\,y=2x-3
\]


\item
\begin{enumerate}
\item \label{4a_popew}R\'{e}soudre par le calcul l'\'{e}quation:
$x^{2}-2x+1=-2x+3$.

\item \label{4b_popew}R\'{e}soudre par le calcul l'\'{e}quation:
$x^{2}-2x+1=2x-3$. (On pourra pour cela factoriser: $x^{2}-4x+4$).

\item Donner une interpr\'{e}tation graphique des r\'{e}sultats des questions
\textbf{\ref{4a_popew}} et \textbf{\ref{4b_popew}}.
\end{enumerate}

\item Tracer sur la figure \ref{0512002029}, la courbe repr\'{e}sentative de
la fonction d\'{e}finie sur l'intervalle~$[-3;5]$ par:
\[
g(x)=-\frac{1}{2}x^{2}+2x+12
\]
On utilisera pour cela un tableau de valeurs.
\end{enumerate}

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%% \psaxes[linewidth=.5pt]{->}(0,0)(-3.5,-1.5)(5.5,16.5)}
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%% %\psplot[plotpoints=100,linestyle=dashed]{-3}{5}{-0.5 x mul 2 add  x mul 12 add}
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%% \caption{}\label{0512002028}
%% \end{figure}%
%

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\end{exercise}


\end{document}