Question

Is `-x^2 +x(x-3)` a quadratic?

Answer 1

Not really. It is equivalent (with no exclusions) to `-3x`, since the terms in `x^2` cancel out.

Of course, you could say that it is of the form `ax^2+bx+c` with `a=0`, `b=-3` and `c=0`, but that does not make it a quadratic any more than it's a cubic or quartic.