Graphing the function y=x^2sin(1/x)

I'm happy to share the code from an old project I worked on with pgfplots. The code includes a plot with multiple functions, including an oscillatory function and a parabola. I have not checked your code but I think that the problem is here: sin(deg(1/x)). Here's the code:

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{arrows}
\begin{document}
\begin{figure}[hp]
\centering
\begin{tikzpicture}[line cap=round, line join=round, >=triangle 45, x=1cm, y=1cm]
\begin{axis}[ 
    axis equal,
    axis lines=middle,  
    xmin=-1, xmax=1,   
    ymin=-.25, ymax=1,    
    xtick={-1,0,1},  
    ytick={0,1},  
    samples=1000,  
    width=12cm,  
    height=8cm,  
    legend pos=north west,
    legend style={fill=gray!10,draw=none,cells={anchor=west}},
    enlargelimits=true
]
\addplot[green, thick, smooth,domain=-0.5:0.5] {x^2*(sin(deg(1/x)))};
\addlegendentry{$y = x^2\sin(1/x)$}
\addplot[magenta, thick, dotted, smooth,domain=-0.5:0.5] {x^2}; 
\addplot[domain=-0.5:0.5, dotted, thick, black] {-x^2};
\addlegendentry{$y=\pm x^2$}

\draw [magenta,thick, fill] (0,0) circle [radius=.5pt, scale=1/0.8];
\end{axis}  
\end{tikzpicture}
\end{figure}
\end{document}

You can use a better tool: happily, also l3fp correctly computes x^2*sin(1/x) as zero when x is zero.

And l3fp assumes radians, which pgfmath doesn't.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usepackage{pgfmath-xfp}

\pgfmxfpdeclarefunction{sqsin}{1}{#1^2*sin(1/#1)}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    axis equal,
    axis lines = middle,
    xlabel = $x$,
    ylabel = $y$,
    xmin = -0.4, xmax = 0.4,
    ymin = -0.4, ymax = 0.4,
    grid = both,
    grid style = {line width=.1pt, draw=gray!10},
    major grid style = {line width=.2pt, draw=gray!50},
    samples = 200,
    legend pos = north west,
    width = 10cm,
    height = 8cm
  ]

    % Plot the curve
    \addplot[domain=-0.5:0.5, thick, blue] {sqsin(x)};
    \addlegendentry{$y = x^2\sin(1/x)$}


    % Tangent line at (1, -2)
    \addplot[domain=-0.5:0.5, thick, red] {x^2};
    \addplot[domain=-0.5:0.5, thick, red] {-x^2};
    \addlegendentry{$y=\pm x^2$}
  \end{axis}
\end{tikzpicture}
\end{document}