Applying linear algebra to non-linear algebra
1. Using linear algebra, find the equation of a parabola passing through all three of these points. 
2. Are there any other parabolas passing through all three of these points? If so, give an example of such a parabola and explain how many there are; if not, explain why there aren't any more. 
3. Would you be able to carry out the methods you used in 1 and 2 for any three distinct points in two dimensions? If so, explain why; if not, what additional requirement(s) would the points have to satisfy to let you do so?