\documentclass[a4paper,12pt]{article}

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\everymath{\displaystyle}
\setlength{\parindent}{0in}

\pagestyle{fancy}
\lhead{GYMASE DE BURIER}
\rhead{1MSt}
\cfoot{}

\begin{document}

\centering
\hspace{2cm}\\ 
\textbf{\large Tableau récapitulatif sur les graphes de fonctions quadratiques}\\[1cm]

\footnotesize
\begin{tabular}{| m{1cm} | >{\centering\arraybackslash} m{7.5cm} | >{\centering\arraybackslash} m{7.5cm} |}

\hline
 & $a>0$ (convexe) & $a<0$ (concave) \\ 
 & Le sommet de la parabole est un minimum &  Le sommet de la parabole est un maximum \\ \hline

$\Delta > 0$ &

\begin{tikzpicture}[scale=0.35]
\coordinate (O) at (0,0);
\def\xmax{8};
\def\max{8};
\def\min{-10};
\def\qmax{7}
\def\qmin{-9};
\foreach \x in {\qmin,..., \qmax}{
\draw[black!40] (\x, \min) -- (\x, \max);}
\foreach \y in{\qmin,..., \qmax}{
\draw[black!40]  (\min , \y) -- (\max, \y );}

\node[below left] at (O) {O};
\node[left] at (0,1) {1};
\node[below] at (1,0) {1};
\draw[very thick] (-0.2, 1) -- (0.2, 1); 
\draw[very thick] (1,-0.2) -- (1, 0.2); 
\fill (0,0) circle (0.5pt); 

\fill (-5/4, -49/8) circle (0.2cm) node[left,fill=white, xshift=-0.1cm]{$\mathcal{S}\left(-\frac{b}{2a}; -\frac{\Delta}{4a}\right)$}; 
\fill (0, -3) circle (0.2cm) node[right, fill=white, xshift=0.1cm]{$\mathcal{H}(0; c)$}; 
\fill (0.5, 0) circle (0.2cm) node[above right, fill=white, xshift=0.1cm]{$\mathcal{Z}_1\left(\frac{-b - \sqrt{\Delta}}{2a}; 0\right)$}; 
\fill (-3, 0) circle (0.2cm) node[above left, fill=white, xshift=-0.1cm]{$\mathcal{Z}_2\left(\frac{-b + \sqrt{\Delta}}{2a}; 0\right)$}; 

\draw[-latex, thick] (0:\min) -- (0:\max) node[right]{x};
\draw[-latex, thick] (90:\min) -- (90:\max) node[above]{y};

\draw[dashed, thick] (-5/4, \min) -- (-5/4,\max);

\clip (\min, \min) rectangle (\max, \max);
\draw[very thick, smooth, domain=\min:\max, smooth, samples=100] plot(\x, {2*(\x)^2 +5*\x - 3});

\end{tikzpicture}
&
\begin{tikzpicture}[scale=0.35]
\coordinate (O) at (0,0);
\def\xmax{8};
\def\max{8};
\def\min{-10};
\def\qmax{7}
\def\qmin{-9};
\foreach \x in {\qmin,..., \qmax}{
\draw[black!40] (\x, \min) -- (\x, \max);}
\foreach \y in{\qmin,..., \qmax}{
\draw[black!40]  (\min , \y) -- (\max, \y );}

\node[below left] at (O) {O};
\node[left] at (0,1) {1};
\node[below] at (1,0) {1};
\draw[very thick] (-0.2, 1) -- (0.2, 1); 
\draw[very thick] (1,-0.2) -- (1, 0.2); 
\fill (0,0) circle (0.5pt); 
\fill (-5/4, 49/8) circle (0.2cm) node[left,fill=white, xshift=-0.1cm]{$\mathcal{S}\left(-\frac{b}{2a}; -\frac{\Delta}{4a}\right)$}; 
\fill (0, 3) circle (0.2cm) node[right, fill=white, xshift=0.1cm]{$\mathcal{H}(0; c)$}; 
\fill (0.5, 0) circle (0.2cm) node[below right, fill=white, xshift=0.1cm]{$\mathcal{Z}_1\left(\frac{-b + \sqrt{\Delta}}{2a}; 0\right)$}; 
\fill (-3, 0) circle (0.2cm) node[below left, fill=white, xshift=-0.1cm]{$\mathcal{Z}_2\left(\frac{-b - \sqrt{\Delta}}{2a}; 0\right)$}; 

\draw[-latex, thick] (0:\min) -- (0:\max) node[right]{x};
\draw[-latex, thick] (90:\min) -- (90:\max) node[above]{y};

\draw[dashed, thick] (-5/4, \min) -- (-5/4,\max);

\clip (\min, \min) rectangle (\max, \max);
\draw[very thick, smooth, domain=\min:\max, smooth, samples=100] plot(\x, {-2*(\x)^2 -5*\x + 3});


\end{tikzpicture} 
\\ \hline

$\Delta = 0$ &

\begin{tikzpicture}[scale=0.35]
\coordinate (O) at (0,0);
\def\xmax{8};
\def\max{8};
\def\min{-10};
\def\qmax{7}
\def\qmin{-9};
\foreach \x in {\qmin,..., \qmax}{
\draw[black!40] (\x, \min) -- (\x, \max);}
\foreach \y in{\qmin,..., \qmax}{
\draw[black!40]  (\min , \y) -- (\max, \y );}

\node[below left] at (O) {O};
\node[left] at (0,1) {1};
\node[below] at (1,0) {1};
\draw[very thick] (-0.2, 1) -- (0.2, 1); 
\draw[very thick] (1,-0.2) -- (1, 0.2); 
\fill (0,0) circle (0.5pt); 
\fill (2, 0) circle (0.2cm) node[below right,fill=white, yshift=-0.12cm, xshift=-0.5cm]{$\mathcal{Z}=\mathcal{S}\left(-\frac{b}{2a}; 0\right)$}; 
\fill (0, 4) circle (0.2cm) node[left, fill=white, xshift=-0.1cm]{$\mathcal{H}(0; c)$};  

\draw[-latex, thick] (0:\min) -- (0:\max) node[right]{x};
\draw[-latex, thick] (90:\min) -- (90:\max) node[above]{y};

\draw[dashed, thick] (2, \min) -- (2,\max);

\clip (\min, \min) rectangle (\max, \max);
\draw[very thick, smooth, domain=\min:\max, smooth, samples=100] plot(\x, {(\x)^2 -4*\x + 4});

\end{tikzpicture}
&
\begin{tikzpicture}[scale=0.35]
\coordinate (O) at (0,0);
\def\xmax{8};
\def\max{8};
\def\min{-10};
\def\qmax{7}
\def\qmin{-9};
\foreach \x in {\qmin,..., \qmax}{
\draw[black!40] (\x, \min) -- (\x, \max);}
\foreach \y in{\qmin,..., \qmax}{
\draw[black!40]  (\min , \y) -- (\max, \y );}

\node[below left] at (O) {O};
\node[left] at (0,1) {1};
\node[below] at (1,0) {1};
\draw[very thick] (-0.2, 1) -- (0.2, 1); 
\draw[very thick] (1,-0.2) -- (1, 0.2); 
\fill (0,0) circle (0.5pt); 
\fill (2, 0) circle (0.2cm) node[above right,fill=white, yshift=0.12cm, xshift=-0.5cm]{$\mathcal{Z}=\mathcal{S}\left(-\frac{b}{2a}; 0\right)$}; 
\fill (0, -4) circle (0.2cm) node[left, fill=white, xshift=-0.1cm]{$\mathcal{H}(0; c)$};  

\draw[-latex, thick] (0:\min) -- (0:\max) node[right]{x};
\draw[-latex, thick] (90:\min) -- (90:\max) node[above]{y};

\draw[dashed, thick] (2, \min) -- (2,\max);

\clip (\min, \min) rectangle (\max, \max);
\draw[very thick, smooth, domain=\min:\max, smooth, samples=100] plot(\x, {-(\x)^2 +4*\x - 4});


\end{tikzpicture} 
\\ \hline

$\Delta < 0$ &

\begin{tikzpicture}[scale=0.35]
\coordinate (O) at (0,0);
\def\xmax{8};
\def\max{8};
\def\min{-10};
\def\qmax{7}
\def\qmin{-9};
\foreach \x in {\qmin,..., \qmax}{
\draw[black!40] (\x, \min) -- (\x, \max);}
\foreach \y in{\qmin,..., \qmax}{
\draw[black!40]  (\min , \y) -- (\max, \y );}

\node[below left] at (O) {O};
\node[left] at (0,1) {1};
\node[below] at (1,0) {1};
\draw[very thick] (-0.2, 1) -- (0.2, 1); 
\draw[very thick] (1,-0.2) -- (1, 0.2); 
\fill (0,0) circle (0.5pt); 
\fill (-2, 2) circle (0.2cm) node[left,fill=white, yshift=0cm, xshift=-0.1cm]{$\mathcal{S}\left(-\frac{b}{2a}; -\frac{\Delta}{4a}\right)$}; 
\fill (0, 4) circle (0.2cm) node[right, fill=white, xshift=0.1cm]{$\mathcal{H}(0; c)$};  

\draw[-latex, thick] (0:\min) -- (0:\max) node[right]{x};
\draw[-latex, thick] (90:\min) -- (90:\max) node[above]{y};

\draw[dashed, thick] (-2, \min) -- (-2,\max);

\clip (\min, \min) rectangle (\max, \max);
\draw[very thick, smooth, domain=\min:\max, smooth, samples=100] plot(\x, {0.5*(\x+2)^2 + 2 });

\end{tikzpicture}
&

\begin{tikzpicture}[scale=0.35]
\coordinate (O) at (0,0);
\def\xmax{8};
\def\max{8};
\def\min{-10};
\def\qmax{7}
\def\qmin{-9};
\foreach \x in {\qmin,..., \qmax}{
\draw[black!40] (\x, \min) -- (\x, \max);}
\foreach \y in{\qmin,..., \qmax}{
\draw[black!40]  (\min , \y) -- (\max, \y );}

\node[below left] at (O) {O};
\node[left] at (0,1) {1};
\node[below] at (1,0) {1};
\draw[very thick] (-0.2, 1) -- (0.2, 1); 
\draw[very thick] (1,-0.2) -- (1, 0.2); 
\fill (0,0) circle (0.5pt); 
\fill (-2, -2) circle (0.2cm) node[left,fill=white, yshift=0cm, xshift=-0.1cm]{$\mathcal{S}\left(-\frac{b}{2a}; -\frac{\Delta}{4a}\right)$}; 
\fill (0, -4) circle (0.2cm) node[right, fill=white, xshift=0.1cm]{$\mathcal{H}(0; c)$};  

\draw[-latex, thick] (0:\min) -- (0:\max) node[right]{x};
\draw[-latex, thick] (90:\min) -- (90:\max) node[above]{y};

\draw[dashed, thick] (-2, \min) -- (-2,\max);

\clip (\min, \min) rectangle (\max, \max);
\draw[very thick, smooth, domain=\min:\max, smooth, samples=100] plot(\x, {-0.5*(\x+2)^2 - 2 });

\end{tikzpicture}
\\ \hline



\end{tabular}

\end{document}
