Two students were working independently on the problem in which 2 points (3,4) and (-3,-2) were provided.
a) Later, two students were asked to determine the parabola passing through same two points, and again students got two different parabolas for answers. Could both students be right?
b) Are two points provided above special, that is, would the answer to (a) change if two other points were provided?
c) How many points do you require to be sure that only 1 parabola passes through given points? Can you prove answer?