\documentclass[tikz,margin=5pt]{standalone}

\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=newest}

\begin{document}

  \begin{tikzpicture}

    \begin{axis}[
        axis lines = center,
        %ticks = none,
        xlabel = {$x_1$},
        ylabel = {$w_1$},
        xmin=-.5, xmax=5,
        ymin=-1, ymax=18,
        %xmin=-.1, xmax=2,
        %ymin=-.1, ymax=4,
        %domain = -.3:2.1,
        %width=.4\textwidth,
        %height=.4\textwidth
      ]
      %\addplot[name path = A, brown!60,samples=100, domain=0:4, no markers, solid, smooth] ({x}, {x^2});
      \addplot[name path = A, samples=100, domain=0:4, solid, smooth] ({x}, {x^2});
      %\draw[name    path = U, red!90] (axis cs: {-.25}, {-1}) -- (axis cs: {4.25}, {17});
      %\draw[name path = A, green!90] (axis cs: {0}, {-1}) -- (axis cs: {4}, {13});
      %\addplot[teal!10,opacity=70] fill between [of = U and A, soft clip={domain=0:4}];
    \end{axis}
  \end{tikzpicture}
\end{document}
