Build with Python: a beginner course where code draws

Three tracks, three outcomes: a prosecutor who declined, a campus process that expelled two students, and a civil suit now under political review. Here is how they fit together.

Substituting a parabola into an ellipse gives a quartic, so the discriminant trick fails. Three derivations lead to the same polynomial in b, with two real roots.

Why 1/x fails as a counterexample, and which two functions give a finite answer from the antiderivative formula while still not being integrable.