I'm doing this math course through correspondence and really the only indication they've given to determine a quadratic function is that the first difference numbers are not constant, while the second difference numbers are constant (same #). Well I'm stuck on this question because it doesn't follow the above rule, plus aren't the points always at the same distance on both sides of the parabola (mirrored)?

Question A says 'confirm' that it is quadratic though, so I'm wondering if it really is, so could someone explain WHY it is, if it is?