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%%  Ein Beispiel der DANTE-Edition
%%  Mathematiksatz mit LaTeX
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%%  Beispiel 10-03-1 auf Seite 215.
%%  Copyright (C) 2018 Herbert Voss
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\begin{document}
\[ \begin{array}{rcll}
y & = & x^{2}+bx+c\\
  & = & x^{2}+2\cdot\dfrac{b}{2}x+c\\
  & = & \underbrace{x^{2}+2\cdot\dfrac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-
      {\left(\dfrac{b}{2}\right)^{2}+c}\\
  &  & \qquad\left(x+{\dfrac{b}{2}}\right)^{2}\\
  & = & \left(x+\dfrac{b}{2}\right)^{2}-\left(\dfrac{b}{2}\right)^{2}+c
  & \left|+\left({\dfrac{b}{2}}\right)^{2}-c\right.\\
    y+\left(\dfrac{b}{2}\right)^{2}-c & = & \left(x+
    \dfrac{b}{2}\right)^{2} & \left|\strut(\textrm{Scheitelpunktform})\right.\\
y-y_{S} & = & (x-x_{S})^{2}\\
S(x_{S};y_{S}) & \,\textrm{bzw.}\,
    & S\left(-\dfrac{b}{2};\,\left(\dfrac{b}{2}\right)^{2}-c\right)
\end{array} \]
\end{document}