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%
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\SetKwIF{Si}{SinonSi}{Sinon}{Si}{alors}{SinonSi}{Sinon}{FinSi}
\SetKwBlock{Trait}{Traitement}{FinTraitement}
\SetKwBlock{TraitSortie}{Traitement et Sortie}{FinTraitement}
\SetKwFor{Pour}{Pour}{faire}{FinPour}
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% contenu de la page de titre
\title{{\bf FONCTIONS DU SECOND DEGRÉ}}
\subtitle{Série 2}
\author{\small{Calcul mental et automatismes -- IREM de Clermont-Ferrand}}
\institute{\texttt{}}
\date{}
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\begin{document}

\begin{frame}
\titlepage 
\end{frame}



%%%%%%%%%%%%%%%%%%%%
%%% Question (1) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (1)}

\begin{texgraph}[name=tabVarQ1_f1, export=pgf, preload="variations.mod", auto=false]
LabelSize:=scriptsize,
dimTab(4,6),
defLargeCol(0,0.9,2,0.25,4,0.75,6,0.25), 
defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","~~~~-\infty","2","+\infty~~~~"),
InitCol1(+1,"f(x)"),
variationsLig(4,"~",+2,"-3",-2,"~"),  
\end{texgraph}

\begin{texgraph}[name=tabVarQ1_f2, export=pgf, preload="variations.mod", auto=false]
LabelSize:=scriptsize,
dimTab(4,6),
defLargeCol(0,0.9,2,0.25,4,0.75,6,0.25), defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","~~~~-\infty","-2","+\infty~~~~"),
InitCol1(+1,"f(x)"),
variationsLig(4,"~",+2,"-3",-2,"~"),  
\end{texgraph}

\begin{texgraph}[name=tabVarQ1_v, export=pgf, preload="variations.mod", auto=false]
LabelSize:=scriptsize,
dimTab(4,6),
defLargeCol(0,0.9,2,0.25,4,0.75,6,0.25), defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","~~~~-\infty","-2","+\infty~~~~"),
InitCol1(+1,"f(x)"),
variationsLig(2,"~",-2,"-3",+2,"~"),  
\end{texgraph}


\begin{frame}
\frametitle{\textbf{Question (1)}}
Soit la fonction $f$ définie sur $\R$ par $f(x)=-5(x+2)^2-3$.

\vspace*{1cm}

{\centering
	\makebox[0pt]{%
	\begin{tabular}{c}
	\begin{tabularx}{\linewidth}{*{3}{>{\centering \arraybackslash}X}}
	\input{tabVarQ1_f1.pgf} & \input{tabVarQ1_v.pgf} & \input{tabVarQ1_f2.pgf}\\
	(a) & (b) & (c)
	\end{tabularx}
	\end{tabular}
	}
	\par
}

\bigskip

\begin{block}{}
Quel est le tableau de variation de cette fonction $f$ ? 
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%% Question (2) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (2)}

\begin{texgraph}[name=tabVarQ2_f1, export=pgf, preload="variations.mod", auto=false]
LabelSize:=scriptsize,
dimTab(4,6),
defLargeCol(0,0.9,2,0.25,4,0.75,6,0.25), defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","~~~~-\infty","-3","+\infty~~~~"),
InitCol1(+1,"f(x)"),
variationsLig(4,"~",+2,"1",-2,"~"),  
\end{texgraph}

\begin{texgraph}[name=tabVarQ2_f2, export=pgf, preload="variations.mod", auto=false]
LabelSize:=scriptsize,
dimTab(4,6),
defLargeCol(0,0.9,2,0.25,4,0.75,6,0.25), defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","~~~~-\infty","-3","+\infty~~~~"),
InitCol1(+1,"f(x)"),
variationsLig(2,"~",-2,"1",+2,"~"),  
\end{texgraph}

\begin{texgraph}[name=tabVarQ2_v, export=pgf, preload="variations.mod", auto=false]
LabelSize:=scriptsize,
dimTab(4,6),
defLargeCol(0,0.9,2,0.25,4,0.75,6,0.25), defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","~~~~-\infty","1","+\infty~~~~"),
InitCol1(+1,"f(x)"),
variationsLig(2,"~",-2,"-3",+2,"~"),  
\end{texgraph}

\begin{frame}
\frametitle{\textbf{Question (2)}}

Soit la fonction $f$ définie sur $\R$ par $f(x)=-3+(x-1)^2$.

\vspace*{1cm}

{\centering
	\makebox[0pt]{%
	\begin{tabular}{c}
	\begin{tabularx}{\linewidth}{*{3}{>{\centering \arraybackslash}X}}
	\input{tabVarQ2_f1.pgf} & \input{tabVarQ2_f2.pgf} & \input{tabVarQ2_v.pgf}\\
	(a) & (b) & (c)
	\end{tabularx}
	\end{tabular}
	}\par
}

\bigskip

\begin{block}{}
Quel est le tableau de variation de cette fonction $f$ ?
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%% Question (3) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (3)}

\begin{texgraph}[name=tabVarQ3_f1, export=pgf, preload="variations.mod", auto=false]
LabelSize:=scriptsize,
dimTab(4,6),
defLargeCol(0,0.9,2,0.25,4,0.75,6,0.25), defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","~~~-\infty","1","+\infty~~~"),
InitCol1(+1,"f(x)"),
variationsLig(2,"~",-2,"-5",+2,"~"),  
\end{texgraph}

\begin{texgraph}[name=tabVarQ3_v, export=pgf, preload="variations.mod", auto=false]
LabelSize:=scriptsize,
dimTab(4,6),
defLargeCol(0,0.9,2,0.25,4,0.75,6,0.25), defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","~~~-\infty","1","+\infty~~~"),
InitCol1(+1,"f(x)"),
variationsLig(4,"~",+2,"-5",-2,"~"),  
\end{texgraph}

\begin{texgraph}[name=tabVarQ3_f2, export=pgf, preload="variations.mod", auto=false]
LabelSize:=scriptsize,
dimTab(4,6),
defLargeCol(0,0.9,2,0.25,4,0.75,6,0.25), defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","~~~-\infty","1","+\infty~~~"),
InitCol1(+1,"f(x)"),
variationsLig(2,"~",["-5",labelstyle:=framed, FillStyle:=full, FillColor:=white, FillOpacity:=1,arrows:=0],-2,"~"),  
\end{texgraph}

\begin{frame}
\frametitle{\textbf{Question (3)}}
Soit la fonction $f$ définie sur $\R$ par $f(x)=-2x^2+4x-7$.

\vspace*{1cm}

{\centering
	\makebox[0pt]{%
	\begin{tabular}{c}
	\begin{tabularx}{\linewidth}{*{3}{>{\centering \arraybackslash}X}}
	\input{tabVarQ3_f1.pgf} & \input{tabVarQ3_f2.pgf} & \input{tabVarQ3_v.pgf}\\
	(a) & (b) & (c)
	\end{tabularx}
	\end{tabular}
	}\par
}

\bigskip

\begin{block}{}
Quel tableau de variation cette fonction $f$ peut-elle avoir ?
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%% Question (4) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (4)}

\begin{texgraph}[name=courbeQ4_v, export=pgf, preload="grid.mod", auto=false]
Fenetre(-5+4*i,2-5*i,1+i),
Marges(0,0,0,0),
size(4),
draw("axeX",[0,1],[Arrows:=1,labelpos:=jump]),
draw("axeY",[0,1],[Arrows:=1,labelpos:=jump]),
NewMac("f","-(%1+2)^2+3"),
draw("cartesian",f(x),[x:=[Xmin,Xmax],Color:=red]),
draw("label","$0$",[anchor:=0,labeldir:=SW]
            ,"$1$",[anchor:=i,labeldir:=West]
            ,"$1$",[anchor:=1,labeldir:=South])
\end{texgraph}

\begin{texgraph}[name=courbeQ4_f1, export=pgf, preload="grid.mod", auto=false]
Fenetre(-5+4*i,2-5*i,1+i),
Marges(0,0,0,0),
size(4),
draw("axeX",[0,1],[Arrows:=1,labelpos:=jump]),
draw("axeY",[0,1],[Arrows:=1,labelpos:=jump]),
NewMac("f","(%1+2)^2-3"),
draw("cartesian",f(x),[x:=[Xmin,Xmax],Color:=red]),
draw("label","$0$",[anchor:=0,labeldir:=SW]
            ,"$1$",[anchor:=i,labeldir:=West]
            ,"$1$",[anchor:=1,labeldir:=South])
\end{texgraph}

\begin{texgraph}[name=courbeQ4_f2, export=pgf, preload="grid.mod", auto=false]
Fenetre(-2+4*i,4-5*i,1+i),
Marges(0,0,0,0),
size(4),
draw("axeX",[0,1],[Arrows:=1,labelpos:=jump]),
draw("axeY",[0,1],[Arrows:=1,labelpos:=jump]),
NewMac("f","-(%1-2)^2+3"),
draw("cartesian",f(x),[x:=[Xmin,Xmax],Color:=red]),
draw("label","$0$",[anchor:=0,labeldir:=SW]
            ,"$1$",[anchor:=i,labeldir:=West]
            ,"$1$",[anchor:=1,labeldir:=South])
\end{texgraph}

\begin{frame}
\frametitle{\textbf{Question (4)}}
Soit la fonction $f$ définie sur $\R$ par $f(x)=-(x+2)^2+3$.

\bigskip

{\centering
	\makebox[0pt]{%
	\begin{tabular}{c}
	\begin{tabularx}{\linewidth}{*{3}{>{\centering \arraybackslash}X}}
	\input{courbeQ4_f1.pgf} & \input{courbeQ4_v.pgf} & \input{courbeQ4_f2.pgf}\\
	(a) & (b) & (c)
	\end{tabularx}
	\end{tabular}
	}\par
}

\bigskip

\begin{block}{}
Quelle est la courbe qui représente la fonction $f$ ?
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%% Question (5) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (5)}

\begin{texgraph}[name=courbeQ5_v, export=pgf, preload="grid.mod", auto=false]
Fenetre(-3+7*i,5-3*i,1+i),
Marges(0,0,0,0),
size(4),
draw("axeX",[0,1],[Arrows:=1,labelpos:=jump]),
draw("axeY",[0,1],[Arrows:=1,labelpos:=jump]),
NewMac("f","%1^2/3-%1"),
draw("cartesian",f(x),[x:=[Xmin,Xmax],Color:=red]),
draw("label","$0$",[anchor:=0,labeldir:=SW]
            ,"$1$",[anchor:=i,labeldir:=West]
            ,"$1$",[anchor:=1,labeldir:=South])
\end{texgraph}

\begin{texgraph}[name=courbeQ5_f1, export=pgf, preload="grid.mod", auto=false]
Fenetre(-3+3*i,5-7*i,1+i),
Marges(0,0,0,0),
size(4),
draw("axeX",[0,1],[Arrows:=1,labelpos:=jump]),
draw("axeY",[0,1],[Arrows:=1,labelpos:=jump]),
NewMac("f","-%1^2/3+%1"),
draw("cartesian",f(x),[x:=[Xmin,Xmax],Color:=red]),
draw("label","$0$",[anchor:=0,labeldir:=SW]
            ,"$1$",[anchor:=i,labeldir:=West]
            ,"$1$",[anchor:=1,labeldir:=South])
\end{texgraph}

\begin{texgraph}[name=courbeQ5_f2, export=pgf, preload="grid.mod", auto=false]
Fenetre(-5+7*i,3-3*i,1+i),
Marges(0,0,0,0),
size(4),
draw("axeX",[0,1],[Arrows:=1,labelpos:=jump]),
draw("axeY",[0,1],[Arrows:=1,labelpos:=jump]),
NewMac("f","%1^2/3+%1"),
draw("cartesian",f(x),[x:=[Xmin,Xmax],Color:=red]),
draw("label","$0$",[anchor:=0,labeldir:=SW]
            ,"$1$",[anchor:=i,labeldir:=West]
            ,"$1$",[anchor:=1,labeldir:=South])
\end{texgraph}

\begin{frame}
\frametitle{\textbf{Question (5)}}
Soit la fonction $f$ définie sur $\R$ par $f(x)=\dfrac13x^2-x$.

\bigskip

{\centering
	\makebox[0pt]{%
	\begin{tabular}{c}
	\begin{tabularx}{\linewidth}{*{3}{>{\centering \arraybackslash}X}}
	\input{courbeQ5_f1.pgf} & \input{courbeQ5_f2.pgf} & \input{courbeQ5_v.pgf}\\
	(a) & (b) & (c)
	\end{tabularx}
	\end{tabular}
	}\par
}

\bigskip

\begin{block}{}
Quelle est la courbe qui représente la fonction $f$ ?
\end{block}
\end{frame}


%%%%%%%%%%%%%%%%%%%%
%%% Question (6) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (6)}

\begin{texgraph}[name=courbeQ6_v, export=pgf, preload="grid.mod", auto=false]
Fenetre(-4.5+4.5*i,2.5-5*i,1+i),
Marges(0,0,0,0),
size(4),
draw("axeX",[0,2],[originpos:=left, Arrows:=1]),
draw("axeY",[0,2],[originpos:=jump, Arrows:=1]),
NewMac("f","-.75*(%1+3)^2-2"),
draw("cartesian",f(x),[x:=[Xmin,Xmax],Color:=red]) 
\end{texgraph}

\begin{texgraph}[name=courbeQ6_f1, export=pgf, preload="grid.mod", auto=false]
Fenetre(-1.5+4.5*i,5.5-5*i,1+i),
Marges(0,0,0,0),
size(4),
draw("axeX",[0,2],[originpos:=left, Arrows:=1]),
draw("axeY",[0,2],[originpos:=jump, Arrows:=1]),
NewMac("f","-.75*(%1-3)^2+2"),
draw("cartesian",f(x),[x:=[Xmin,Xmax],Color:=red]) 
\end{texgraph}

\begin{texgraph}[name=courbeQ6_f2, export=pgf, preload="grid.mod", auto=false]
Fenetre(-1.5+4.5*i,5.5-5*i,1+i),
Marges(0,0,0,0),
size(4),
draw("axeX",[0,2],[originpos:=left, Arrows:=1]),
draw("axeY",[0,2],[originpos:=jump, Arrows:=1]),
NewMac("f","-.75*(%1-3)^2-2"),
draw("cartesian",f(x),[x:=[Xmin,Xmax],Color:=red]) 
\end{texgraph}


\begin{frame}
\frametitle{\textbf{Question (6)}}
Soit la fonction $f$ définie sur $\R$ par $f(x)=-\dfrac{3}{4}(x-3)^2+2$.

\bigskip

{\centering
	\makebox[0pt]{%
	\begin{tabular}{c}
	\begin{tabularx}{\linewidth}{*{3}{>{\centering \arraybackslash}X}}
	\input{courbeQ6_v.pgf} & \input{courbeQ6_f1.pgf} & \input{courbeQ6_f2.pgf}\\
	(a) & (b) & (c)
	\end{tabularx}
	\end{tabular}
	}\par
}

\bigskip

\begin{block}{}
Quelle est la courbe qui représente la fonction $f$ ?
\end{block}
\end{frame}

\begin{frame}
	\begin{block}{}
	\begin{center}
	{\Large
	Pour chacune des questions suivantes, déterminer \underline{la} bonne réponse.
	}
	\end{center}
	\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%% Question (7) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (7)}

\begin{frame}
\frametitle{\textbf{Question (7)}}

Soit la fonction $f$ définie sur $\R$ par $f(x)=5(x-1)^2+3.$

\vspace*{0.5cm}

\begin{block}{}
La fonction $f$ est :
\begin{center}
	\setstretch{1.5}
	\begin{tabular}{cl}
		(a) & décroissante sur l'intervalle $]-\infty~;~+\infty[$ ;\\
		(b) & décroissante sur l'intervalle $]-\infty~;~1]$ ;\\
		(c) & décroissante sur l'intervalle $]-\infty~;~3]$.
	\end{tabular}
	\setstretch{1}
\end{center}
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%% Question (8) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (8)}

\begin{frame}
\frametitle{\textbf{Question (8)}}

Soit la fonction $f$ définie sur $\R$ par $f(x)=-2(x+3)^2-1.$

\vspace*{0.5cm}

\begin{block}{}
La fonction $f$ est :
\begin{center}
	\setstretch{1.5}
	\begin{tabular}{cl}
		(a) & décroissante sur l'intervalle $]-\infty~;~+\infty[$ ;\\
		(b) & décroissante sur l'intervalle $[+3~;~+\infty[$ ;\\
		(c) & décroissante sur l'intervalle $[-3~;~+\infty[$.
	\end{tabular}
	\setstretch{1}
\end{center}
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%
%%% Question (9) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (9)}

\begin{frame}
\frametitle{\textbf{Question (9)}}
Soit la fonction $f$ définie sur $\R$ par $f(x)=(x-4)^2+2.$

\vspace*{0.5cm}

\begin{block}{}
La fonction $f$ est :
\begin{center}
	\setstretch{1.5}
	\begin{tabular}{cl}
		(a) & croissante sur l'intervalle $]-\infty~;~+\infty[$ ;\\
		(b) & croissante sur l'intervalle $[4~;~+\infty[$ ;\\
		(c) & croissante sur l'intervalle $[2~;~+\infty[$.
	\end{tabular}
	\setstretch{1}
\end{center}
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%
%%% Question (10) %%%
%%%%%%%%%%%%%%%%%%%%%
\section{Question (10)}

\begin{frame}
\frametitle{\textbf{Question (10)}}

Soit la fonction $f$ définie sur $\R$ par $f(x)=-3+2(x+1)^2.$

\vspace*{0.5cm}

\begin{block}{}
La fonction $f$ est :
\begin{center}
	\setstretch{1.5}
	\begin{tabular}{cl}
		(a) & décroissante sur l'intervalle $]-\infty~;~+\infty[$ ;\\
		(b) & croissante sur l'intervalle $[5~;~+\infty[$ ;\\
		(c) & décroissante sur l'intervalle $]-\infty~;~2]$.
	\end{tabular}
	\setstretch{1}
\end{center}
\end{block}
\end{frame}

\begin{texgraph}[preload="ornaments.mod", name=fin, export=pgf, auto=false]
Fenetre(-3+0.5*i,3-0.5*i,1+i),
Marges(0,0,0,0),
S:=Loadvectorian(72),
Drawvectorian(-2, S, [width:=2]),
S:=Loadvectorian(73),
Drawvectorian(2, S, [width:=2]),
LabelSize:=Huge, Label(0, "FIN") 
\end{texgraph}

\begin{frame}
\begin{center} {\Huge 
\input{fin.pgf}
} \end{center}
\end{frame}

\end{document}




















%%%%%%%%%%%%%%%%%%%%
%%% Question (3) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (3)}

\begin{texgraph}[name=tabVarQ3, export=pgf, preload="variations.mod", auto=false]
dimTab(4,6),
defLargeCol(0,1), defHautLig(3,0),
Cadre(1,1,4,6), traitH(1), traitV(1),
InitLig1("x","-\infty","\sqrt2","+\infty"),
InitCol1(+1,"f(x)"),
variationsLig(4,"~",+2,"5",-2,"~"),  
\end{texgraph}

\begin{frame}
\frametitle{\textbf{Question (3)}}
Soit la fonction $f$ définie sur $\R$ dont le tableau de variation est le suivant :

\bigskip

\begin{center}
	\input{tabVarQ3.pgf}
\end{center}

\bigskip

\begin{block}{}
Quelle est l'expression de $f(x)$ ?
\begin{center}
	\setstretch{1.5}
	\begin{tabular}{cl}
		(a) & $f(x)= 5(x-1)^2+\sqrt{2}$ ;\\
		(b) & $f(x)= 3(x-5)^2+ \sqrt{2}$ ;\\
		(c) & $f(x)= 2\left(x- \sqrt{2}\right)^2+5$.
	\end{tabular}
	\setstretch{1}
\end{center}
\end{block}
\end{frame}



%%%%%%%%%%%%%%%%%%%%
%%% Question (6) %%%
%%%%%%%%%%%%%%%%%%%%
\section{Question (6)}

\begin{texgraph}[name=courbeQ6, export=pgf, preload="grid.mod", auto=false]
Fenetre(-2.5+3.5*i,4.5,1+i),
Marges(0,0,0,0),
size(6),
draw("axeX",[0,1],[originpos:=left, Arrows:=1]),
draw("axeY",[0,1],[originpos:=jump, Arrows:=1]),
NewMac("f","sqrt(2)*%1^2-2*%1+1"),
draw("cartesian",f(x),[x:=[Xmin,Xmax]])  
\end{texgraph}

\begin{frame}
\frametitle{\textbf{Question (6)}}
Soit la fonction $f$ définie sur $\R$ dont la représentation graphique est la suivante :

\bigskip

\begin{center}
	\input{courbeQ6.pgf}
\end{center}

\bigskip

\begin{block}{}
Quelle est l'expression de $f(x)$ ?
\begin{center}
	\setstretch{1.5}
	\begin{tabular}{cl}
		(a) & $f(x)= -3x+1$ \phantom{$25x+1$}\\
		(b) & $f(x)= 3x^2+1$ \phantom{$0,5x+1$}\\
		(c) & $f(x)= \sqrt{2}x^2-0,5x+1$
	\end{tabular}
	\setstretch{1}
\end{center}
\end{block}
\end{frame}

