Put down the y values in a row:

   1   3   6   10

Find the first successive differences by subtracting 
neighboring numbers, and write their differences 
between and below them:

   1   3   6   10
     2   3   4

Find the second successive differences again by 
subtracting neighboring numbers, and writing their 
differences between and below them:

   1   3   6   10
     2   3   4
       1   1

That took 2 lines of differences until all the differences
were all the same, in this case, 1. 

So we know that we need an equation of degree 2.



Plug in all three points:

Plug in (1,1) 




Plug in (2,3) 




Plug in (3,6) 




You don't need the fourth point.

So you have the system:



Solve that system and get:

,  and 

Therefore:



becomes:



or



Factor out  on the right:



To take  is the same as dividing by :



Edwin