Remove labels with pgfplots

Question

How to remove extreme labels on each axis ?

Why does the shape of the curve is not limited to the upper edge of the grid ?

I find that the curve is not very smooth, especially at the apex of the parabola. I am a user Metapost, and I do not have this trouble if I draw the same curve.

   \documentclass[11pt,a4paper]{article} 
   \usepackage{geometry}
   \geometry{margin=1in} 
   \usepackage{tikz}
   \usepackage{tkz-euclide}
   \usetikzlibrary{calc,shapes.misc}
   \usepackage{pgfplots}
   \pgfplotsset{compat=1.8}

   \begin{document}
   \begin{center}
   \begin{tikzpicture}
   \begin{axis}[
     restrict x to domain=-3:3, xmax=3, xmin=-3,
     restrict y to domain=-3:5, ymax=5, ymin=-3,
     x=1cm,
     y=1cm,
     axis lines=middle,
     line width = 0.35mm,
     xtick={-3,-2,-1,0,1,2,3},
     ytick={-3,-2,-1,0,1,2,3,4,5},
     grid=major,
     >=stealth,
     compat=newest,
     x label style={at={(axis description cs:0.98,0.32)},anchor=south},
     y label style={at={(axis description cs:0.5,0.98)},rotate=-90,anchor=east},
     xlabel={$x$},
     ylabel={$y$}, 
      ]
     \addplot [red,line width=1,smooth,domain=-3:3] {2*x^2-x-2} ;
     \node[below right] at (1,-1){A}; 
     \node[below left] at (0,0){$0$}; 
     \node[fill=red,circle,scale=0.3] at (1,-1){};
     \end{axis}
     \end{tikzpicture} 
     \end{center}
     \end{document}

Answer 1

Adding additional samples seems to make the curve go all the way to the top of the grid. This is achieved by adding samples=300, to your axis.

To remove the labels but not remove the ticks as you requested you can employ the xticklabelsand yticklabels options to specify where to place the labels. The \empty bits make the label blank and if you don't include them the labels will shift.

  \documentclass[11pt,a4paper]{article} 
   \usepackage{geometry}
   \geometry{margin=1in} 
   \usepackage{tikz}
   \usepackage{tkz-euclide}
   \usetikzlibrary{calc,shapes.misc}
   \usepackage{pgfplots}
   \pgfplotsset{compat=1.8}

   \begin{document}
   \begin{center}
   \begin{tikzpicture}
   \begin{axis}[
     restrict x to domain=-3:3, xmax=3, xmin=-3,
     restrict y to domain=-3:5, ymax=5, ymin=-3,
     x=1cm,
     y=1cm,
     axis lines=middle,
     line width = 0.35mm,
     xtick={-2,-1,0,1,2},
     xticklabels={\empty,-2,-1,0,1,2},
     ytick={-2,-1,0,1,2,3,4},
     yticklabels={\empty,-2,-1,0,1,2,3,4,\empty},
     grid=major,
     samples=300,
     >=stealth,
     compat=newest,
     x label style={at={(axis description cs:0.98,0.32)},anchor=south},
     y label style={at={(axis description cs:0.5,0.98)},rotate=-90,anchor=east},
     xlabel={$x$},
     ylabel={$y$}, 
      ]
     \addplot [red,line width=1,smooth,domain=-3:3] {2*x^2-x-2} ;
     \node[below right] at (1,-1){A}; 
     \node[below left] at (0,0){$0$}; 
     \node[fill=red,circle,scale=0.3] at (1,-1){};
     \end{axis}
     \end{tikzpicture} 
     \end{center}
     \end{document}