Trying to graph a parabola and horizontal lines in pgf plot

Question

I am trying to graph the following graph and so far I only have code to graph the parabola, could someone help me graph the dashed horizontal and vertical lines.
begin{tikzpicture}
begin{axis}[
    axis lines = middle,
    xlabel = $x$,
    ylabel = {$f(x)$},
    yticklabels=empty,
    xticklabels=empty,
]

addplot [
    domain=0:10, 
    samples=100, 
    color=red,
]
{x^2};
end{axis}
end{tikzpicture}

Zarko · Accepted Answer

You can insert function equation, which you like to draw, directly to addplot command, for example:
addplot +[ultra thick, color=purple, domain=0:2] {x^2};

or define function in `axis options as is done in MWE (Minimal Working Example) below.
Point on function curve you can define as (<x>,{f(x){) or you calculate manually or use in your case select x=1 where f(x) = (x^2) is 1 (as is used in MWE below.
MWE should work also with older version of pgfplots, but not the oldest as compat=v1.11.
documentclass[border=3.141592]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.18}

begin{document}
    begin{tikzpicture}
begin{axis}[
declare function = {f(x)=(x)^2);},
    axis lines=left,
    xlabel = $x$,
    ylabel = $f(x)$,
    xmin=0,    xmax=2.2,         xtick=empty,
    ymin=0,    ymax=4.4,         ytick=empty,
    domain=0:2,
    no marks,
    every axis plot post/.append style={ultra thick, color=magenta,},
            ]
addplot    {f(x)} node[right,text=black] {$x^2$};
draw[dashed] (0,1) -- (1,1) node[above left] {$b$}
                             node[below right] {$a$}
                   -- (1,0); 
end{axis}
    end{tikzpicture}
end{document}

Trying to graph a parabola and horizontal lines in pgf plot

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