\documentclass[12pt]{scrartcl}
\usepackage[T1]{fontenc}
\usepackage{tgpagella}
\usepackage{xcolor}
\usepackage{ulem}
\usepackage{geometry}
\usepackage{scrlayer-scrpage}
\geometry{letterpaper}
\usepackage{hyperref}

\hypersetup{
    colorlinks=true,
    linkcolor=blue,
    filecolor=magenta,      
    urlcolor=isaac-red,
    pdftitle={F25MB6\_Notes\_Greene\_Isaac},
    pdfauthor={Isaac Greene},
    pdfpagemode=FullScreen
}
\urlstyle{same}

\definecolor{isaac-red}{HTML}{C52947}
\definecolor{isaac-blue}{HTML}{0E4385}

\newcommand\sectionuline{%
  \bgroup\markoverwith{\textcolor{isaac-red}{\rule[-0.5ex]{2pt}{1.7pt}}}%
  \ULon%
}
\newcommand\subsectionuline{%
  \bgroup\markoverwith{\textcolor{isaac-blue}{\rule[-0.5ex]{2pt}{1.7pt}}}%
  \ULon%
}

\clearpairofpagestyles

\setkomafont{subsubsection}{\usefont{T1}{qpl}{b}{n}}
\setkomafont{subsection}{\usefont{T1}{qpl}{m}{n}\large}
\setkomafont{section}{\usefont{T1}{qpl}{b}{n}\Large}
\setkomafont{part}{\usefont{T1}{qpl}{b}{n}\LARGE}
\addtokomafont{part}{\subsectionuline}
\addtokomafont{section}{\sectionuline}
\addtokomafont{subsection}{\subsectionuline}
\addtokomafont{subsubsection}{\sectionuline}

\setlength{\parindent}{0pt}
\setlength{\parskip}{12pt}

\lohead{F25MB6\_Notes\_Greene\_Isaac}
\lofoot{No AI used <\href{http://ig7.us/ai}{ig7.us/ai}>. Built with \LaTeX.\\Work available under the Esoteric Common License <\href{http://ig7.us/license}{ig7.us/license}>.}
\ohead*{\pagemark}

\begin{document}
\part*{MTH122:13 Notes}
These notes have been digitally typeset and reassembled from scratch notes. 
\tableofcontents

\section{2025-09-03}
Notes on domain and range\footnote{Dr. Filiz Dogru was our sub on Friday (Sep 5) because Mrs. Brott was out. She has been a math professor at GV for over 23 years.}
Find domain and range. Domain is x-axis, and range is y-axis.
y-intercept = $f(0)$ or $(0, c)$ 
x-intercept = $\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=0$

Direction (end behavior) = if a > 0, as $x \longrightarrow \infty$, graph goes up.

Axis of symmetry and $x_{vertex} = \frac{-b}{2a}$ in standard form but simply "h" in vertex form.
$y_{vertex} = f(x)$ where $x = \frac{-b}{2a}$

\begin{equation}
f(x) = 2x^{2}-x-1
\end{equation}
\begin{equation}
f(x) = \frac{1}{2*2} = \frac{1}{4} = 0.25
\end{equation}
\begin{equation}
Vertex = (0.25, -1.125)
\end{equation}
\begin{equation}
\frac{+1\pm\sqrt{-1^{2}-4(2)(-1)}}{2(2)}
\end{equation}
\begin{equation}
\frac{1\pm\sqrt{1+8}}{4}
\end{equation}
\begin{equation}
\frac{1\pm\sqrt{9}}{4} = \frac{1\pm3}{4} = \frac{-2}{4} and \frac{4}{4}\ so\ x=\{-0.5, 1\}
\end{equation}

\section{2025-09-10}
\begin{equation}(x+2)(x+3)=0\end{equation} $\\6x^{2}+x-1=0\\
x^{2}+5x+6x=0$
\hrule
$5x^{2}-7x+2=0$
\begin{enumerate}
\item When $a \neq 1$, multiply first and last term, ($5x^{2}\cdot2=10x$)
\item Find two numbers that multiply to (first * last) and add to the middle term
\item Replace middle term with the found numbers
\item Split the polynomial in half, like $5x^{2}-5x-2x+2$ becomes $(5x^{2}-5x) | (-2x+2)$
\item Factor each group
\end{enumerate}
$\frac{(5x^{2}}{5x}-\frac{5x)}{5x}$
\end{document}
