<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%% 
%%  An UIT Edition example
%% 
%%  Example 10-03-1 on page 202.
%% 
%%  Copyright (C) 2010 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 
%% 
%% ==== 
% Show page(s) 1
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\documentclass[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{375.57637pt}
\AtBeginDocument{\setlength\parindent{0pt}}
\StartShownPreambleCommands
\usepackage{amsmath}
\StopShownPreambleCommands
\begin{document}
\[
\begin{array}{rcll}
y &amp; = &amp; x^{2}+bx+c\\
  &amp; = &amp; x^{2}+2\times\dfrac{b}{2}x+c\\
  &amp; = &amp; \underbrace{x^{2}+2\times\dfrac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-
      {\left(\dfrac{b}{2}\right)^{2}+c}\\
  &amp;  &amp; \qquad\left(x+{\dfrac{b}{2}}\right)^{2}\\
  &amp; = &amp; \left(x+\dfrac{b}{2}\right)^{2}-\left(\dfrac{b}{2}\right)^{2}+c
  &amp; \left|+\left({\dfrac{b}{2}}\right)^{2}-c\right.\\
    y+\left(\dfrac{b}{2}\right)^{2}-c &amp; = &amp; \left(x+
    \dfrac{b}{2}\right)^{2} &amp; \left|\strut(\textrm{vertex form})\right.\\
y-y_{S} &amp; = &amp; (x-x_{S})^{2}\\
S(x_{S};y_{S}) &amp; \,\textrm{or}\,
    &amp; S\left(-\dfrac{b}{2};\,\left(\dfrac{b}{2}\right)^{2}-c\right)
\end{array}
\]
\end{document}
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