Centrar verticalmente los textos de las celdas de la tabla

Question

¿Cómo se hace que el contenido de esta celda esté centrado verticalmente?

Aquí está el resultado actual basado en el siguiente código. Gracias

\documentclass[]{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{pgfplots}
\renewcommand{\thesection}{\arabic{section}}
\usepackage{mathtools}
\usepackage{cancel}
\usepackage{pgfplots}
\usepackage{amsmath}
\newtheorem{theorem}{THEOREM}
\newtheorem{proof}{PROOF}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning,shapes,fit,calc}
\usepackage{amssymb}
\usetikzlibrary{patterns}
\usepackage{fancyhdr}
\usepackage{bigints}
\usepackage{color}
\usepackage{tcolorbox}
\usepackage{color,xcolor }
\usepackage{booktabs,array}
\usepackage{hyperref}
\usepackage{graphicx}
\usetikzlibrary{arrows}
\usepackage{polynom}
\DeclareMathOperator{\rank}{rank}
\makeatletter
\newenvironment{sqcases}{%
    \matrix@check\sqcases\env@sqcases
}{%
\endarray\right.%
}
\def\env@sqcases{%
    \let\@ifnextchar\new@ifnextchar
    \left\lbrack
    \def\arraystretch{1.2}%
    \array{@{}l@{\quad}l@{}}%
}
\begin{document}
The graph of the quadratic function $y=ax^2$
\begin{center}
\setlength\arraycolsep{6pt} % default is "5pt"
$\begin{array}{>{\centering\arraybackslash}m{1in}cc}
\midrule
\text{ } &
a>0 &
a<0\\
\midrule
\text{graph} &
\pgfplotsset{every axis/.append style={
axis x line=middle,    % put the x axis in the middle
axis y line=middle,    % put the y axis in the middle
axis line style={<->}, % arrows on the axis
title={$y$},
xlabel={$x$},          % default put x on x-axis
ylabel={},          % default put y on y-axis
ticks=none
}}
\begin{tikzpicture}
\begin{axis}[
xmin=-1.3,xmax=1.3,ymin=-0.5,ymax=1.5
]
\addplot[thick,samples=20,domain=-1:1] {x^2};
\end{axis}
\end{tikzpicture} &
\pgfplotsset{every axis/.append style={
axis x line=middle,    % put the x axis in the middle
axis y line=middle,    % put the y axis in the middle
axis line style={<->}, % arrows on the axis
title={$y$},
xlabel={$x$},          % default put x on x-axis
ylabel={},          % default put y on y-axis
ticks=none
}}
\begin{tikzpicture}
\begin{axis}[
xmin=-1.3,xmax=1.3,ymin=-1.5,ymax=0.5
]
\addplot[thick,samples=20,domain=-1:1] {-x^2};
\end{axis}
\end{tikzpicture}
\\
\midrule
\text{behaviour} &
\text{increasing for } x>0, \text{decreasing for }x<0 &
\text{decreasing for } x>0, \text{increasing for }x<0
\\\\
\midrule
\text{vertext} &
\multicolumn{2}{c}{(0,0)}\\
\\
\midrule
\text{size} &
\multicolumn{2}{c}{\text{If the value of }|a|\quad
\begin{sqcases}
\text{increases, the wider the shape of the parabola}\\
\text{decreases, the narrower the shape of the parabola}\\
\end{sqcases}}\\
\midrule
\end{array}$
\newline\newline
\end{center}
\end{document}

Answer 1

Está perfectamente centrado. La única razón por la que obtienes son dos filas vacías. He comentado lo espurio \\en la parte relevante de su código (líneas 82-91).

\midrule
\text{behaviour} &
\text{increasing for } x>0, \text{decreasing for }x<0 &
\text{decreasing for } x>0, \text{increasing for }x<0
\\%\\
\midrule
\text{vertext} &
\multicolumn{2}{c}{(0,0)}%\\
\\
\midrule

Además, envolver los tikzpicture entornos en un \raisebox-0.5\height{…}, you can centre thegráfico text. Example for the firsttikzpicture` (líneas 58-64):

\raisebox{-0.5\height}{\begin{tikzpicture}
\begin{axis}[
xmin=-1.3,xmax=1.3,ymin=-0.5,ymax=1.5
]
\addplot[thick,samples=20,domain=-1:1] {x^2};
\end{axis}
\end{tikzpicture}} &