pgfplots: use foreach inside addplot

Question

I want to add a bunch of evenly spaced vertical lines to a plot using \foreach.

I can do it like this:

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}

\begin{document}

\begin{tikzpicture}

    \begin{axis}[
        axis lines=left,
        scaled ticks=false,
        xtick=\empty,
        ytick=\empty,
        ymin=0,
    ]

    \addplot[samples=100,domain=0:10] {(x-5)^2 + 20};

    \addplot coordinates {\foreach \x in {1,...,9}  (\x,0) (\x,40)};

    \end{axis}

\end{tikzpicture}

\end{document}  

And I get the following plot:

However, I want all of the lines to be part of the same plot; something like this:

\addplot coordinates {\foreach \x in {1,...,9}  (\x,0) (\x,40)};

or this:

\addplot {\foreach \x in {1,...,9} coordinates (\x,0) (\x,40)};

But neither of these compiles. Is it possible to use \foreach inside \addplot, and if so, what's the correct syntax?

Edit: I want the plot to be something like this:

which I generated with the following snippet:

\addplot coordinates {
    (1,0) (1,40)

    (2,0) (2,40)

    (3,0) (3,40)

    (4,0) (4,40)
};

But I want to do it using a for-type loop.

By the way, the reason I'm doing this is to be able to drop lines from the curve to the x-axis and label them. I plan to make the vertical lines invisible, then find the intersections of the curve the vertical lines, and then use the intersection points as coordinates for visible lines that start at the curve. If there's a more efficient way to do that (which seems like a pretty common thing to do), I'm all ears. Edit: I'm reading the function from a file, not generating it using a formula.

Answer 1

To avoids expansion issues with \foreach, pgfplots offers \pgfplotsinvokeforeach which can be used without problems; also, you can easily draw your lines from the curve to the axis using the function (no need to find intersections points); declaring the function from the beginning also simplifies the code:

The code:

\documentclass[border=5]{standalone}
\usepackage{pgfplots}
%\pgfplotsset{compat=1.12}

\pgfmathdeclarefunction{myfunct}{1}{%
  \pgfmathparse{(#1-5)^2 + 20}%
}

\begin{document}    
\begin{tikzpicture} 
    \begin{axis}[%
        ,axis lines=left
        ,xtick=\empty
        ,ytick=\empty
        ]
        \addplot[samples=100,domain=0:10] {myfunct(x)};
        \pgfplotsinvokeforeach{1,...,9}{
            \addplot coordinates { (#1,0) (#1,40) };}
    \end{axis}  
\end{tikzpicture}\qquad
\begin{tikzpicture} 
    \begin{axis}[%
        ,axis lines=left
        ,xtick=\empty
        ,ytick=\empty
        ]
        \addplot[samples=100,domain=0:10] {myfunct(x)};
        \pgfplotsinvokeforeach{1,...,9}{
            \addplot coordinates { (#1,0) (#1,{myfunct(#1)}) };
            \node[above=5pt] at (axis cs:#1,{myfunct(#1)}) {\pgfmathprint{myfunct(#1)}};
            }
    \end{axis}  
\end{tikzpicture}   

\end{document} 

Update

Using the same idea, name the path for the curve and inside \pgfplotsinvokeforeach draw the lines and name them; find the intersection points and draw the desired lines with the required labels:

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.10}

\usepackage{filecontents}
\begin{filecontents*}{mydata.dat}
-6 36
-5 25
-4 16
-3 9
-2 4
-1 1
0 0
1 1
2 4
3 9
4 16
5 25
6 36
\end{filecontents*}


\begin{document}

\begin{tikzpicture}

\begin{axis}[
  axis lines=left,
  scaled ticks=false,
  xtick=\empty,
  ytick=\empty,
  ymin=0,
]
\addplot[no marks,smooth,name path=curve] table {mydata.dat};
\pgfplotsinvokeforeach{-6,...,6}{
  \addplot[draw=none,name path={line#1}] coordinates  { (#1,0) (#1,40) };
  \path[name intersections={of=curve and line#1,by={point#1}}];
  \draw[red]
    (axis cs:#1,0) -- (point#1) node[above,black] {#1};
}
\end{axis}

\end{tikzpicture}

\end{document} 

Answer 2

The correct syntax (or at least a syntax which works) can be seen below:

% arara: pdflatex

\documentclass[border=5]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}

\begin{document}    
\begin{tikzpicture} 
    \begin{axis}[%
        ,axis lines=left
        ,xtick=\empty
        ,ytick=\empty
        ]
        \addplot[samples=100,domain=0:10] {(x-5)^2 + 20};
        \foreach \x in {1,...,9}
        {\edef\temp{\noexpand\addplot coordinates { (\x,0) (\x,40)};}\temp}
    \end{axis}  
\end{tikzpicture}   
\end{document} 

Answer 3

From last paragraph on your question, I understand you want something like this:

\documentclass[border=2mm]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}

\begin{document}

\begin{tikzpicture}

    \begin{axis}[
        axis lines=left,
        scaled ticks=false,
        xtick=\empty,
        ytick=\empty,
        ymin=0,
        declare function={myfunction(\t)=(\t-5)^2+20;}
    ]

    \addplot[samples=100,domain=0:10] {myfunction(x)};

    \foreach \x in {1,...,9}
        {\edef\temp{\noexpand\addplot coordinates { (\x,{myfunction(\x)})};}\temp}

     \draw (axis cs:3,{myfunction(3)})--++(90:2cm);
     \draw[red] (axis cs:2,{myfunction(2)})--(axis cs:7,{myfunction(7)});
    \end{axis}

\end{tikzpicture}

\end{document}