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% Document Info
\author{Lady's Notenook (Lady\_Notenook)}
\pdfinfo{
  /Title (algebra.pdf)
  /Creator (Cheatography)
  /Author (Lady's Notenook (Lady\_Notenook))
  /Subject (Algebra Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Algebra Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Lady's Notenook (Lady\_Notenook)} via \textcolor{DarkBackground}{\uline{cheatography.com/203562/cs/43368/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Lady's Notenook (Lady\_Notenook) \\
  \uline{cheatography.com/lady-notenook} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 12th May, 2024.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\end{multicols}}




\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.53827 cm} x{2.43873 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Linear Functions}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Standard/General form:}} & f(x) = ax + b \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Slope/rate of change}} & a/m = y2-y1/x2-x1 \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{y-intercepy}} & b \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
{\bf{Slope intercept form}} & f(x) = mx + b \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
{\bf{Point-slope form}} & y-y1 = y2-y1/x2-x1 (x-x1) \tn 
% Row Count 9 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Variable occurs to the {\bf{first power only}}} \tn 
% Row Count 10 (+ 1)
% Row 6
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\mymulticolumn{2}{x{5.377cm}}{The graph is a line} \tn 
% Row Count 11 (+ 1)
% Row 7
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\mymulticolumn{2}{x{5.377cm}}{Constant rate of change} \tn 
% Row Count 12 (+ 1)
% Row 8
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Positive rate of change & Slope Upward \tn 
% Row Count 14 (+ 2)
% Row 9
\SetRowColor{white}
Negative rate of change & Slope Downward \tn 
% Row Count 16 (+ 2)
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\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.4931 cm} x{3.4839 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Effects of Changing h and k}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{vertex form: (h, k)} \tn 
% Row Count 1 (+ 1)
% Row 1
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Changing h & x = h; horizontal shift \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Changing k & y = k; vertical shift \tn 
% Row Count 3 (+ 1)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} x{4.4793 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{How to solve {\bf{Polynomial Functions}}}}  \tn
% Row 0
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 & 1. Factor out  (no exponent is inside the parenthesis) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
 & 2. Set the function equal to zero \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
 & 3. Solve for x \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
 & 4. Find Multiplicity \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
 & 5. Find x and y intercept. Use 0, if imaginary use 2 numbers that are symmetric to each other \tn 
% Row Count 8 (+ 3)
% Row 5
\SetRowColor{white}
 & 6. Plot out the x you solve on step 3 sa x-axis \tn 
% Row Count 10 (+ 2)
% Row 6
\SetRowColor{LightBackground}
 & 7. Plot the x and y intercepts on step 5 \tn 
% Row Count 12 (+ 2)
% Row 7
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 & 7 Check if tama ang graph using ang leadig coefficient \tn 
% Row Count 14 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Create Quadratic func. with the Vertex and points}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{1. Substitute the vertex to the function} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{2}{x{5.377cm}}{2. Substitute x and y intercept} \tn 
% Row Count 2 (+ 1)
% Row 2
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\mymulticolumn{2}{x{5.377cm}}{3. Solve for a} \tn 
% Row Count 3 (+ 1)
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\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Formula:}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{a\textasciicircum{}3\textasciicircum{} + b\textasciicircum{}3\textasciicircum{} = (a+b) (a\textasciicircum{}2\textasciicircum{} - ab + b\textasciicircum{}2\textasciicircum{})} \tn 
% Row Count 1 (+ 1)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.73735 cm} x{2.23965 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Quadratic Functions}}  \tn
% Row 0
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{\bf{General form}} & f(x) = ax + bx + c \tn 
% Row Count 1 (+ 1)
% Row 1
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{\bf{Standard form}} & f(x) = a(x - h) + k \tn 
% Row Count 3 (+ 2)
% Row 2
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{\bf{Vertex}} & (h, k) \tn 
% Row Count 4 (+ 1)
% Row 3
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\mymulticolumn{2}{x{5.377cm}}{Polynomial function of degree {\bf{2}}} \tn 
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% Row 4
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\mymulticolumn{2}{x{5.377cm}}{Graph of f is a {\bf{parabola}}} \tn 
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% Row 5
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Parabola opens upward & a \textgreater{} 0 (+) : minimum \tn 
% Row Count 8 (+ 2)
% Row 6
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parabola opens downward & a \textless{} 0 (-) : maximum \tn 
% Row Count 10 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{How to graph Quadratic Functions}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{1. Expressing in standard form by completing the square or using (x = -b/2a} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{2}{x{5.377cm}}{2. Find Vertex} \tn 
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% Row 2
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\mymulticolumn{2}{x{5.377cm}}{3. Identify max/min} \tn 
% Row Count 4 (+ 1)
% Row 3
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\mymulticolumn{2}{x{5.377cm}}{4. Find x and y intercept} \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{5. Plot Vertex and points} \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{6. Find domain ad range  {\bf{Note:}} Domain is always real number} \tn 
% Row Count 8 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Even Coefficient Graph}}  \tn
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\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/lady-notenook_1715533822_440561113_466536502510683_7332127948507141193_n.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Same Direction sa start and end }}               If Positive: Upward        If Negative: Downward}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Odd Coefficient}}  \tn
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\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/lady-notenook_1715534341_441146710_794105875981462_368734178380906538_n.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Opposite Directions}}  If Postive:ascending, If Negative: descending}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.28942 cm} x{2.68758 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Polynomial Function}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Example sa form}} & f(x) = 2x\textasciicircum{}3\textasciicircum{} - 6x\textasciicircum{}2\textasciicircum{} + 10 \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Exponents & Always positive exponents and no  fractional exponents \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
Coefficients & 2, -6 \tn 
% Row Count 6 (+ 1)
% Row 3
\SetRowColor{white}
Constant \seqsplit{coefficient/Constant} term & 10 \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Leading coefficient & 2 \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
Leading term & 2x\textasciicircum{}3\textasciicircum{} \tn 
% Row Count 11 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{It is continuous; graph has no breaks or holes} \tn 
% Row Count 12 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Note:}} Dapat always sunod ang mga terms depende sa \# of degree or exponents. If kulangan butangan ug 0 \textasciicircum{}ang exponent\textasciicircum{}} \tn 
% Row Count 15 (+ 3)
% Row 8
\SetRowColor{LightBackground}
{\bf{Higher exponent (even)}} & Steeper, flatter \tn 
% Row Count 17 (+ 2)
% Row 9
\SetRowColor{white}
{\bf{Higher exponent (odd)}} & wider \tn 
% Row Count 19 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Remainder Theorem}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/lady-notenook_1715534730_442651105_1444439349544937_7563779638244606843_n.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{If a polynomial p(x) is divided by the binomial x - a, the remainder obtained is p(a)}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Factor Theorem}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/lady-notenook_1715535715_441162236_802631441425527_3544786373503338169_n.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{C is a zero of p if and only x - c is a factor of P(x)}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}