I'm considering the following set $$M=\{(x,y)\in \Bbb{R}^2: y(y^2-x)=0\}$$ And I want to show that this is not a submanifold of $\Bbb{R}^2$. So it is clear that the critical point is $(0,0)$ but I thought that maybye there is a simple trick how to draw such a graph $$y(y^2-x)=0$$ Therefore I wanted to ask you if there is something like a general or very useful trick so that I can think really geometrically about such an equation.
Thanks for your help.