118 lines
2.8 KiB
TeX
118 lines
2.8 KiB
TeX
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\title{Polynômes du 2e degré - Cours}
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\tribe{1ST}
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\date{Mars 2023}
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\pagestyle{empty}
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\begin{document}
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\setcounter{section}{1}
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\section{Représentation graphique}
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\begin{definition}[Parabole]
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Soit $f(x) = ax^2 + bx + c$ un polynôme du second degré.
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La représentation graphique de $f$ s'appelle une \textbf{parabole}.
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\begin{tabular}{cc}
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\begin{tikzpicture}[yscale=.4, xscale=0.8]
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\tkzInit[xmin=-5,xmax=5,xstep=1,
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ymin=-5,ymax=10,ystep=1]
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\tkzAxeXY
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\tkzFct[domain = -5:5, line width=1pt]{x*x-x+1}
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\end{tikzpicture}
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&
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\begin{tikzpicture}[yscale=.4, xscale=0.8]
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\tkzInit[xmin=-5,xmax=5,xstep=1,
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ymin=-5,ymax=10,ystep=1]
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\tkzAxeXY
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\tkzFct[domain = -5:5, line width=1pt]{-x*x-x+3}
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\end{tikzpicture} \\
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Cas où $a > 0$ les branches sont orientées vers le haut. &
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Cas où $a < 0$ les branches sont orientées vers le bas.
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\end{tabular}
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\end{definition}
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\section{Fonctions particulières}
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Dans le programme de première ST, seules 3 formes de polynômes du 2nd degré sont à savoir étudier et reconnaître.
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\begin{center}
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\Large
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\textbf{$x \mapsto ax^2$}
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\end{center}
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\begin{tabular}{cc}
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\begin{tikzpicture}[yscale=.4, xscale=2]
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\tkzInit[xmin=-2,xmax=2,xstep=1,
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ymin=-5,ymax=10,ystep=1]
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\tkzAxeXY
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\end{tikzpicture}
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&
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\begin{tikzpicture}[yscale=.4, xscale=1.3]
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\tkzInit[xmin=-3,xmax=3,xstep=1,
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ymin=-10,ymax=5,ystep=1]
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\tkzAxeXY
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\end{tikzpicture} \\
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f(x) = 2x^2 &
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f(x) = -3x^2 &
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\end{tabular}
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\pagebreak
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\begin{center}
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\Large
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\textbf{$x \mapsto ax^2 + b$}
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\end{center}
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\begin{tabular}{cc}
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\begin{tikzpicture}[yscale=.4, xscale=2]
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\tkzInit[xmin=-2,xmax=2,xstep=1,
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ymin=-5,ymax=10,ystep=1]
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\tkzAxeXY
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\end{tikzpicture}
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&
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\begin{tikzpicture}[yscale=.4, xscale=1.3]
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\tkzInit[xmin=-3,xmax=3,xstep=1,
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ymin=-10,ymax=5,ystep=1]
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\tkzAxeXY
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\end{tikzpicture} \\
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f(x) = 2x^2 + 2 &
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f(x) = -3x^2 + 4&
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\end{tabular}
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\vspace{3cm}
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\begin{center}
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\Large
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\textbf{$x \mapsto a(x - x_1)(x - x_2)$}
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\end{center}
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\begin{tabular}{cc}
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\begin{tikzpicture}[yscale=.4, xscale=2]
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\tkzInit[xmin=-2,xmax=2,xstep=1,
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ymin=-5,ymax=10,ystep=1]
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\tkzAxeXY
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\end{tikzpicture}
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&
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\begin{tikzpicture}[yscale=.4, xscale=1.3]
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\tkzInit[xmin=-3,xmax=3,xstep=1,
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ymin=-10,ymax=5,ystep=1]
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\tkzAxeXY
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\end{tikzpicture} \\
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f(x) = 2(x-2)(x+1) &
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f(x) = -3(x+2)(x-1)&
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\end{tabular}
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\afaire{Tracer l'allure des fonctions sur les graphiques}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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