\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}