如何绘制如图所示的抛物线割线？

Question

我想画这个图

我尝试过 Geogebra

\documentclass[12pt]{standalone}
\usepackage{fouriernc}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\draw[line width=1.2pt,->,color=black] (-2.5,0.) -- (2.5,0.);
\foreach \x in {-2.,-1.,1.,2.}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt);
\draw[color=black] (2.3,0.031) node [anchor=south west] { $x$};
\draw[line width=1.2pt,->,color=black] (0.,-0.5) -- (0.,5.);
\foreach \y in {,1.,2.,3.,4.}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt);
\draw[color=black] (0.025,4.835) node [anchor=west] {$y$};
\clip(-3.5,-0.5) rectangle (3.5,5.);
\draw[line width=1.2pt,smooth,samples=100,domain=-3.5:3.5] plot(\x,{(\x)^(2.0)});
\draw [domain=-3.5:3.5] plot(\x,{(--2.-3.*\x)/-1.});
\draw [fill=black] (1.,1.) circle (2.0pt);
\draw[color=black] (1.3,0.939) node {$A_0$};
\draw [fill=black] (2.,4.) circle (2.0pt);
\draw[color=black] (2.4,4) node {$A_n$};
\draw [fill=black] (0.667,0.) circle (2.0pt);
\draw[color=black] (1,-0.3) node {$M_n$};
\end{tikzpicture}
\end{document}

现在我想用pgfplots，我试过

\documentclass{standalone}
\usepackage{pgfplots}
\def\FunctionF(#1){(#1)^2}%
\begin{document}
\begin{tikzpicture}
\begin{axis}[
        axis y line=center,
        axis x line=middle, 
        axis on top=true,
        xmin=-2.5,
        xmax=2.5,
        ymin=-1,
        ymax=4.5,
        height=5.0cm,
        width=5.0cm,
        grid,
        xtick={-2,...,2},
        ytick={-1,0,...,5},
    ]
    \addplot [domain=-5:5, samples=50, mark=none, black] {\FunctionF(x)};
\end{axis}
\end{tikzpicture}
\end{document}

我得到了

如何绘制正割 A_nA_0M_n

Answer 1

使用pgfplots最新版本（1.13）：

\documentclass[border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{intersections}

\def\FunctionF(#1){(#1)^2}%

\begin{document}
    \begin{tikzpicture}[
    dot/.style = {red, opacity=0.5, 
                  every node/.style={right=1pt, text=black, opacity=1,
                                     fill=white, inner sep=1pt, 
                                     rounded corners=5pt, font=\footnotesize}
                  }
                    ]
\begin{axis}[
        axis y line=center,
        axis x line=middle,
%        axis on top=true,
        xmin=-2.5,
        xmax=2.8,
        ymin=-1.5,
        ymax=4.5,
        height=5.0cm,
        width=5.0cm,
        grid,
        tick label style={font=\scriptsize},
        xtick={-2,...,2},
        ytick={-1,0,...,5},
    ]
\addplot[domain=-5:5, samples=50, mark=none, black, smooth,
          name path=A] {\FunctionF(x)};
\draw[red,name path=B] (0.5,-0.5) -- (2.16,4.5);
\path[name path=C] (0,0) -- (2,0);
\fill [name intersections={of=A and B, by={a,b}},dot]
      (a) circle (1.2pt) node {$A_0$}
      (b) circle (1.2pt) node {$A_n$};
\fill [name intersections={of=B and C, by=c},dot]
      (c) circle (1.2pt) node {$M_n$};
\end{axis}
    \end{tikzpicture}
\end{document}