An ordered quadruple (y₁,y₂,y₃,y₄) is quadratic if there exists realnumbers a, b, and c such that yn = an²+ bn + c

for n=1,2,3,4

Prove that if 16 numbers are placed in a 4x4 grid such that all four rows are quadratic

and the first three columns are also quadratic then the fourth column must also be quadratic.

(We say that a row is quadratic if its entries, in order, are quadratic. We say the same

for a column.)