Not able to plot parabolas in an array

Question

The following two TikZ environments should give similar displays. I am trying to get five graphs of parabolas, each on the Cartesian plane, and to put a label of a.), b.), c.), d.), or e.) at the upper left corner of each graph - outside the TikZ environment.

The first display uses options in the axis environment, like naming the first plot plot1 and moving the second plot with respect to the first plot with at={($(plot1.east)+(1cm,0)$)}. Except for placing the labels a.), b.), c.), d.), and e.), it is the display that I want. The second uses the adjustbox package. Each graph is too big and the parabolas on each Cartesian plane is artificially shifted. The graphs are displayed in the array that I want, and the labels a.), b.), c.), d.), or e.) seem to be positioned correctly, though.

\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{adjustbox}
\usepackage{mathtools}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}

\noindent This is the left margin. \vskip1.25mm

\begin{tikzpicture}
  \begin{axis}[name=plot1,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-9,ymax=9,
    restrict y to domain=-9:9,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
    ]
    \addplot[samples=201,domain=-3:3,blue] {5*x^(2)};
  \end{axis}
  \begin{axis}[name=plot2,at={($(plot1.east)+(1cm,0)$)},anchor=west,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-9,ymax=9,
    restrict y to domain=-9:9,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
    ]
    \addplot[samples=201,domain=-3:3,blue] {-5*x^(2) + 3};
  \end{axis}
  \begin{axis}[name=plot3,at={($(plot1.south)-(0,1cm)$)},anchor=north,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-9,ymax=9,
    restrict y to domain=-9:9,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
  ]
    \addplot[samples=201,domain=-3:3,blue] {-5*(x^(2) - x)};
  \end{axis}
  \begin{axis}[name=plot4,at={($(plot2.south)-(0,1cm)$)},anchor=north,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-9,ymax=9,
    restrict y to domain=-9:9,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
    ]
    \addplot[samples=201,domain=-3:3,blue] {5*(x^(2) + x)};
  \end{axis}
    \begin{axis}[name=plot5,at={($(plot3.south)-(0,1cm)$)},anchor=north,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-6,ymax=6,
    restrict y to domain=-6:6,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
    ]
    \addplot[samples=201,domain=-3:3,blue] {-5*x^(2) - 0.5)};
  \end{axis}
\end{tikzpicture}


\vfill
\pagebreak


\noindent This is the left margin. \vskip1.25mm

a.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]
\addplot[samples=201,domain=-3:3,blue] {5*x^(2)};\end{axis}
\end{tikzpicture}}
%
b.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]\addplot[samples=201,domain=-3:3,blue] {-5*x^(2) + 3};\end{axis}
\end{tikzpicture}}
%
c.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]\addplot[samples=201,domain=-3:3,blue] {-5*(x^(2) - x};\end{axis}
\end{tikzpicture}}
%
d.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]\addplot[samples=201,domain=-3:3,blue] {5*(x^(2) + x)};\end{axis}
\end{tikzpicture}}
%
e.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]\addplot[samples=201,domain=-3:3,blue] {-5*x^(2) - 0.5};\end{axis}
\end{tikzpicture}}
\hspace{\fill}

\end{document}

Answer 1

One solution is to use the scale option for the tikzpicture environment to reduce the size of the plots. I have not looked for the reason for the off positions graphs. You need to check very carefully for missmatch in plotting area and the graph plotted .

\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{adjustbox}
\usepackage{mathtools}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}

a.) \adjustbox{valign=t}{\begin{tikzpicture}[scale=.25]
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]
\addplot[samples=201,domain=-3:3,blue] {5*x^(2)};\end{axis}
\end{tikzpicture}}
%
b.) \adjustbox{valign=t}{\begin{tikzpicture}[scale=.25]
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]\addplot[samples=201,domain=-3:3,blue] {-5*x^(2) + 3};\end{axis}
\end{tikzpicture}}
%
c.) \adjustbox{valign=t}{\begin{tikzpicture}[scale=.25]
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]\addplot[samples=201,domain=-3:3,blue] {-5*(x^(2) - x};\end{axis}
\end{tikzpicture}}
%
d.) \adjustbox{valign=t}{\begin{tikzpicture}[scale=.25]
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]\addplot[samples=201,domain=-3:3,blue] {5*(x^(2) + x)};\end{axis}
\end{tikzpicture}}
%
e.) \adjustbox{valign=t}{\begin{tikzpicture}[scale=.25]
%These commands plot the second parabola on the Cartesian plane.
\draw[draw=gray!30,latex-latex] (0,9) +(0,0.5) node[above right] {$y$} -- (0,-9) -- +(0,-0.5);
\draw[draw=gray!30,latex-latex] (-3,0) +(-0.5,0) -- (3,0) -- +(0.5,0) node[below right] {$x$};
\begin{axis}[hide axis]\addplot[samples=201,domain=-3:3,blue] {-5*x^(2) - 0.5};\end{axis}
\end{tikzpicture}}
\hspace{\fill}

\end{document}

Here is an alternate way to display parabolas. You only need to look at the pgfplots manual regarding options of the axis environment to see the other possibilities.

\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{adjustbox}
\usepackage{mathtools}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}
\noindent This is the left margin. \vskip1.25mm

a.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\begin{axis}[grid=none,
      mark = none, 
      xmin = -3, ymin = -45,
      xmax = 3,ymax = 45,
      axis lines*=middle,
      enlargelimits=upper,
      clip=false]
\addplot[samples=201,domain=-3:3,blue] {5*x^(2)};\end{axis}
\end{tikzpicture}}
%
b.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\begin{axis}[grid=none,
      mark = none, 
      xmin = -3, ymin = -45,
      xmax = 3,ymax = 45,
      axis lines*=middle,
      enlargelimits=upper,
      clip=false]
\addplot[samples=201,domain=-3:3,blue] {-5*x^(2) + 3};\end{axis}
\end{tikzpicture}}
\par
c.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\begin{axis}[grid=none,
      mark = none, 
      xmin = -3, ymin = -45,
      xmax = 3,ymax = 45,
      axis lines*=middle,
      enlargelimits=upper,
      clip=false]
\addplot[samples=201,domain=-3:3,blue] {-5*(x^(2) - x};\end{axis}
\end{tikzpicture}}
%
d.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\begin{axis}[grid=none,
      mark = none, 
      xmin = -3, ymin = -45,
      xmax = 3,ymax = 45,
      axis lines*=middle,
      enlargelimits=upper,
      clip=false]
\addplot[samples=201,domain=-3:3,blue] {5*(x^(2) + x)};\end{axis}
\end{tikzpicture}}
\par
e.) \adjustbox{valign=t}{\begin{tikzpicture}
%These commands plot the second parabola on the Cartesian plane.
\begin{axis}[grid=none,
      mark = none, 
      xmin = -3, ymin = -45,
      xmax = 3,ymax = 45,
      axis lines*=middle,
      enlargelimits=upper,
      clip=false]
\addplot[samples=201,domain=-3:3,blue] {-5*x^(2) - 0.5};\end{axis}
\end{tikzpicture}}

\end{document}

Diagram using the first half of your code.

\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{adjustbox}
\usepackage{mathtools}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\begin{document}

\noindent This is the left margin. \vskip1.25mm
\begin{tikzpicture}
  \begin{axis}[name=plot1,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-9,ymax=9,
    restrict y to domain=-9:9,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
    ]
    \addplot[samples=201,domain=-3:3,blue] {5*x^(2)};
    \node at (axis cs:-4.5,14) [anchor= north west] {a.)};
  \end{axis}
  \begin{axis}[name=plot2,at={($(plot1.east)+(1cm,0)$)},anchor=west,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-9,ymax=9,
    restrict y to domain=-9:9,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
    ]
    \addplot[samples=201,domain=-3:3,blue] {-5*x^(2) + 3};
    \node at (axis cs:-4.5,14) [anchor= north west] {b.)};
  \end{axis}
  \begin{axis}[name=plot3,at={($(plot1.south)-(0,1cm)$)},anchor=north,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-9,ymax=9,
    restrict y to domain=-9:9,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
  ]
    \addplot[samples=201,domain=-3:3,blue] {-5*(x^(2) - x)};
    \node at (axis cs:-4.5,14) [anchor= north west] {c.)};
  \end{axis}
  \begin{axis}[name=plot4,at={($(plot2.south)-(0,1cm)$)},anchor=north,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-9,ymax=9,
    restrict y to domain=-9:9,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
    ]
    \addplot[samples=201,domain=-3:3,blue] {5*(x^(2) + x)};
    \node at (axis cs:-4.5,14) [anchor= north west] {d.)};
  \end{axis}
    \begin{axis}[name=plot5,at={($(plot3.south)-(0,1cm)$)},anchor=north,height=5cm,width=5cm,
    axis lines=middle,
    xmin=-3,xmax=3,samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-6,ymax=6,
    restrict y to domain=-6:6,
    enlargelimits={abs=0.5cm},
    axis line style={latex-latex},
    xtick={\empty},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
    ]
    \addplot[samples=201,domain=-3:3,blue] {-5*x^(2) - 0.5)};
    \node at (axis cs:-4.5,9) [anchor= north west] {e.)};
  \end{axis}
\end{tikzpicture}

\end{document}