如何在不禁用网格的情况下隐藏轴环境内的轴标签（其中一些除外）？

Question

假设你想画一个图：

\documentclass[dvipsnames]{article}
\usepackage{pgfplots}
\usetikzlibrary{babel,calc,backgrounds,quotes,angles,patterns,decorations.markings,intersections,arrows,arrows.meta}
\pgfplotsset{compat=newest}                       
\usepgfplotslibrary{fillbetween}

\begin{document}


\begin{tikzpicture}
  \begin{axis}[
                axis lines = middle,
                axis line style = {-Latex[round],very thick},
                % enlargelimits = true,
                grid = both,
                grid style={help lines},
                xmin = -4,
                ymin = -3.1,
                xmax = 4,
                ymax = 4,
                xtick = {-3, ..., 3},
                ytick = {-3, ..., 3},
                xlabel style={below right},
                ylabel style={above left},
                x tick label style={below left},
                samples = 100,
                axis on top=true,
                xlabel = {$x$}, 
                ylabel = {$y$},
              ]
    \coordinate (O) at (0, 0);
    
    \addplot[very thick, color=Mahogany] {-x^2 + 2};

  \end{axis}
\end{tikzpicture}

\end{document}

结果是：

如何做出一些奇特的改变：

1. 使 x 的右下方有勾号标签表示负 x，使 x 的左下方有勾号标签表示正 x；

2. 仅显示这些点的刻度标签：(0, 0)、(1, 0)、(0, 1)、(-1, 0)、(0, -1)？如果我更改 xtick = {-3, ..., 3} 和 ytick = {-3, ..., 3}，它将更改网格，但我希望将其保留为 {-3, ..., 3) 刻度。

Answer 1

编辑：

第一次尝试时，根据 OP 评论，显然我没有理解问题。第二次尝试是基于猜测，但我不确定想要的结果是什么...

\documentclass[dvipsnames, margin=3mm]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{arrows.meta,
%
                babel % for languages issues, not needed in this MWE
                } % other libraries are not used
\pgfplotsset{compat=1.17}
%\usepgfplotslibrary{fillbetween} % not used

\begin{document}
    \begin{tikzpicture}
\begin{axis}[
        width=9cm,  % enlarged image width
    axis lines = middle,
    axis line style = {-Latex[round], very thick},
    % grid,
    xmin = -3.5,    xmax = 3.5,
    ymin = -3.5,    ymax = 3.5,
    xtick = {-3,...,3},
        % added, for tick labels placements
        tick style = {major tick length=3mm, 
                      semithick, 
                      color=black},
        xticklabels={,,$-1$, , , , },
        xticklabel style = {inner sep=2pt,
                            anchor=north west,
                            font=\footnotesize},
        extra x ticks={0,1},                
        extra x tick labels={0,1},
        extra x tick style={tick label style={xshift=-0.9em}},
        yticklabels=\empty,                  
        extra y ticks={-1,1},                
    xlabel = {$x$},
    ylabel = {$y$},
    xlabel style={below right},
    ylabel style={above left},
    axis on top,
        samples = 100,  %
             ]
\addplot[very thick, color=Mahogany] {-x^2 + 2};
\end{axis}
    \end{tikzpicture}
\end{document}