begin{tikzpicture}
fill (0, -1) circle (0.1);
% 1.28 is the approximate zero of the black function
draw[very thick] (0, 0) -- (textwidth*0.4/1.5*1.28, 0);
begin{axis}[
    ticks=none,
    domain=0:1.5,
    xmin=0,
    xmax=1.5,
    ymin=0,
    x=textwidth*0.4/1.5, % I thought this would make it work
    axis lines=left,
    xlabel={$r$ color{red}$r^2$},
    ylabel=$m$,
    y label style={at={(axis description cs:0.15, 0.5)}, anchor=south},
    x label style={at={(axis description cs:0.5, 0.1)}},
    axis equal,
]
addplot[mark=none, thick] (x, {1 - x^2 + x/2});
addplot[mark=none, color=red] (x^2, {1 - x^2 + x/2});
end{axis}
end{tikzpicture}