= Solution
The zero set consists of the three lines $x=0$, $y=0$ and $y=x-1$. Their pairwise intersections are
$$
\boxed{(0,0),\quad(1,0),\quad(0,-1).}
$$
The bounded <triangle> has $0\leq x\leq1$ and $x-1\leq y\leq0$. Its edges and interior <contours> are shown below.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1-triangular-contours.png]
{title=Negative contours inside the zero triangle, with outward boundary gradients and the interior minimum}
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