TikZ Plotting: Braces between tickmarks

Question

What is the best way to draw braces between tick marks? It would be convenient to assign nodes at tick marks, is this doable?

The best method for placement that I have right now is a guess-and-check.

MWE:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{patterns,decorations.pathreplacing}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
    axis x line = middle,
    axis y line = middle,
    xticklabels={}
    ]
\addplot [domain=-1:5] { -x * (x-4) };
\end{axis}
\draw [thick,decoration={brace,mirror},decorate] (1.2,3) -- (5.7,3) node[midway,below,yshift=-.1cm] {4};
\end{tikzpicture}

\end{document}

Answer 1

Below I present three levels of improvement:

1. You can move the \draw inside the axis environment and use the axis cs coordinate system which gives you access to the coordinates of the plot; also, you can use the raise option to shift the brace:

   \documentclass{article}
   \usepackage{pgfplots}
   \usetikzlibrary{patterns,decorations.pathreplacing}
   \pgfplotsset{compat=1.10}
   
   \begin{document}
   
   \begin{tikzpicture}
   \begin{axis}[
       axis x line = middle,
       axis y line = middle,
       xticklabels={}
       ]
   \addplot [domain=-1:5] { -x * (x-4) };
   \draw [thick,decoration={brace,mirror,raise=5pt},decorate] 
     (axis cs:0,0) --
       node[below=7pt] {4} 
     (axis cs:4,0);
   \end{axis}
   \end{tikzpicture}
   
   \end{document}
   

   

2. You don't have to know beforehand the coordinates for the intersection points; you can let the intersections library do the calculations for you:

   \documentclass{article}
   \usepackage{pgfplots}
   \usetikzlibrary{patterns,decorations.pathreplacing,intersections}
   \pgfplotsset{compat=1.10}
   
   \begin{document}
   
   \begin{tikzpicture}
   \begin{axis}[
       axis x line = middle,
       axis y line = middle,
       xticklabels={},
       samples=100
       ]
   \addplot[name path=curve,domain=-1:5] { -x * (x-4) };
   \addplot[name path=line,domain=-1:5,forget plot] {0};
   \draw[
     name intersections={of=curve and line, by={a,b}},
     thick,
     decoration={brace,mirror,raise=5pt},decorate
   ] 
     (a) --
       node[below=7pt] {4} 
     (b);
   \end{axis}
   \end{tikzpicture}
   
   \end{document}
   

3. Finally you can also use the calc library and the lengthconvert package, for example, so the length (4) is also automatically calculated:

   \documentclass{article}
   \usepackage{lengthconvert}
   \usepackage{pgfplots}
   \usetikzlibrary{patterns,decorations.pathreplacing,intersections,calc}
   \pgfplotsset{compat=1.10}
   
   \begin{document}
   
   \begin{tikzpicture}
   \begin{axis}[x=1cm,
       axis x line = middle,
       axis y line = middle,
       xticklabels={},
       samples=100
       ]
   \addplot[name path=curve,domain=-1:5] { -x * (x-4) };
   \addplot[name path=line,domain=-1:5,forget plot] {0};
   \draw[
     name intersections={of=curve and line, by={a,b}},
     decoration={brace,mirror,raise=5pt},
     decorate
   ]
     let \p1 = ($ (a) - (b) $),
         \n2 = {veclen(\x1,\y1)}
     in
     (a) --
       node[below=7pt] {\Convert[precision=1,number-only=true]{\n2}} 
     (b);
   \end{axis}
   \end{tikzpicture}
   
   \end{document}