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| author | Florian Fischer <florian.fischer@muhq.space> | 2024-11-06 11:03:55 +0100 |
|---|---|---|
| committer | Florian Fischer <florian.fischer@muhq.space> | 2024-11-06 11:03:55 +0100 |
| commit | 06e4a22c8b6f86cf3d782cd9d9981a17e7f8002b (patch) | |
| tree | 55e0eee36b1965ed3f8e5d6893eaab075ee06057 /Mathe/24_25/11/05/9E/handout.tex | |
| parent | 6ce8694de7a136e2dc86ec98ff5b4e5a18f63233 (diff) | |
| download | unterricht-06e4a22c8b6f86cf3d782cd9d9981a17e7f8002b.tar.gz unterricht-06e4a22c8b6f86cf3d782cd9d9981a17e7f8002b.zip | |
add my past math lessons
Diffstat (limited to 'Mathe/24_25/11/05/9E/handout.tex')
| -rw-r--r-- | Mathe/24_25/11/05/9E/handout.tex | 79 |
1 files changed, 79 insertions, 0 deletions
diff --git a/Mathe/24_25/11/05/9E/handout.tex b/Mathe/24_25/11/05/9E/handout.tex new file mode 100644 index 00000000..a521f061 --- /dev/null +++ b/Mathe/24_25/11/05/9E/handout.tex @@ -0,0 +1,79 @@ +\documentclass[a5paper]{handout} +\csname endofdump\endcsname +\usepackage{pgfplots} + +\renewcommand{\baselinestretch}{1.5} +\title{} +\begin{document} +\thispagestyle{empty} +\makedate + +\begin{tabular}{p{0.6\textwidth} p{0.4\textwidth}} +\vspace{-2.75cm} +Graphen der Funktion $f:x\mapsto x^2$\solution{$+y_s$} \newline sind um \solution{$y_s$~~~} in y-Richtung verschoben. \newline +Ihr Scheitelpunkt liegt bei \solution{$S(0|y_s)$} & +\begin{tikzpicture} +\begin{axis}[ + x=0.5cm, y=0.5cm, + axis x line=center, + axis y line=center, + xtick={-2,...,2}, + ytick={0,...,4}, + xlabel={$x$}, + ylabel={$y$}, + xlabel style={below right}, + ylabel style={above right}, + ymin=-1.2, ymax=5.5, + xmin=-3, xmax=3, + grid=both, + unbounded coords=discard +] + \addplot[domain=-2.3:2.3, samples=50, gray, thick] (\x, {\x^2}); + \solution{\addplot[domain=-2.3:2.3, samples=50, orange, thick] (\x, {\x^2+1});} + \solution{\addplot[domain=-2.3:2.3, samples=50, magenta, thick] (\x, {\x^2-1});} +\end{axis} +\node[anchor=west] at (2.5, 1.9) {\scriptsize \textcolor{gray}{$\bm{f(x) = x^2}$}}; +\node[anchor=west] at (2.5, 0.9) {\scriptsize \textcolor{orange}{$\bm{f_2(x)=x^2+1}$}}; +\node[anchor=west] at (2.5, 1.4) {\scriptsize \textcolor{magenta}{$\bm{f_1(x)=x^2-1}$}}; +\end{tikzpicture} +\\ +\end{tabular} + +\begin{tabular}{p{0.4\textwidth} p{0.6\textwidth}} +\begin{tikzpicture} +\begin{axis}[ + x=0.5cm, y=0.5cm, + axis x line=center, + axis y line=center, + xtick={-2,...,2}, + ytick={0,...,4}, + xlabel={$x$}, + ylabel={$y$}, + xlabel style={below right}, + ylabel style={above right}, + ymin=-1.2, ymax=5.5, + xmin=-3, xmax=3, + grid=both, + unbounded coords=discard +] + \addplot[domain=-2.3:2.3, samples=50, gray, thick] (\x, {\x^2}); + \solution{\addplot[domain=-2.3:2.3, samples=50, orange, thick] (\x, {(\x+1)^2});} + \solution{\addplot[domain=-2.3:2.3, samples=50, magenta, thick] (\x, {(\x-1)^2});} +\end{axis} +\node[anchor=west] at (-2.1, 2.8) {\scriptsize \textcolor{gray}{$\bm{f(x) = x^2}$}}; +\node[anchor=west] at (-2.1, 2.3) {\scriptsize \textcolor{orange}{$\bm{f_1(x)=(x+1)^2}$}}; +\node[anchor=west] at (-2.1, 1.8) {\scriptsize \textcolor{magenta}{$\bm{f_2(x)=(x-1)^2}$}}; +\end{tikzpicture} +& \vspace{-2.75cm} Graphen der Funktion $f:x\mapsto (x\solution{-x_s~~~})^2$ sind um \solution{$x_s$~~~} in x-Richtung verschoben. +Ihr Scheitelpunkt liegt bei \solution{$S(0|y_s)$} \\ +\end{tabular} + +\begin{merke} +Die Darstellung einer quadratischen Funktion der Form +{\setlength{\abovedisplayskip}{2pt} +\setlength{\belowdisplayskip}{2pt} +\[ f:x\mapsto \solution{a(x-x_s)^2+y_s} \]} +nennt man \solution{Scheitelpunktform.} \\ +Ihr Scheitelpunkt $(x_s|y_s)$ kann vom Term direkt abgelesen werden. +\end{merke} +\end{document} |
