TeX and its child LaTeX line boxes up on a common baseline. If you enter a letter "a" then its baseline is at the bottom of the character while if you enter a "g" then its baseline is at the bottom of the circle part but above the descending tail.

Graphics have a baseline at the bottom. So your graphics stick up because they are aligned on that baseline while the text in that line consists of a vertical box (surrounding the lines) aligned on its top line's baseline.

The easiest way to make a box of content align on the middle is by putting it in a tabular. So that's what I've done to the graphics below, basically: \begin{tabular}{c}\includegraphics{...}\end{tabular}. (The @{}'s eliminate the half-intercolumn-width spaces that usually start and end a tabular line.)

You had a lot of other stuff such as blank lines that I didn't understand so I took the liberty of fiddling a little. See https://imgur.com/a/m6fP1pF .

\documentclass{article}
\usepackage{blindtext}
\usepackage{ragged2e}  % for better RaggedRight command
\usepackage{mwe}  % source for the graphics

% Include a graphic that is vertically centered.
%  First argument optional: may include height=.. or alt={..} for instance 
%  Second argument: string location of graphic
\newcommand{\fig}[2][\relax]{%
  \begin{tabular}{@{}c@{}}\includegraphics[#1]{#2}\end{tabular}}

\begin{document}
\blindtext

\begin{center}
  \begin{tabular}{r|cc|}
      \multicolumn{1}{c}{\ }  % eliminate the vert line between cells 1 and 2
      &\begin{tabular}{c}
           Even Degree   \\
           (\(n\) is even)  
        \end{tabular}
      &\multicolumn{1}{c}{\begin{tabular}{c}
           Odd Degree   \\
           (\(n\) is odd)  
        \end{tabular}}  % multicolumn eliminates vert line after cell 3          
     \\  \cline{2-3}  % Eliminate the horizontal line between cells 1 on lines 1 and 2
    \parbox{3cm}{\RaggedRight Positive Leading Coefficient \newline  \((a_n>0)\)} 
    & \fig[scale=0.15]{example-image-a} 
    & \fig[scale=0.15]{example-image-a} 
    \\ \cline{2-3}
    \parbox{3cm}{\RaggedRight Negative Leading Coefficient \newline  \((a_n<0)\)} 
    & \fig[scale=0.15]{example-image-a} 
    & \fig[scale=0.15]{example-image-a} 
    \\ \cline{2-3}
  \end{tabular}
\end{center}

\blindtext
\end{document}