When we have consecutive values, f(10), f(11), f(12), f(13), f(14), we can make a difference table to determine the degree of f as a polynomial. A quadratic will have a constant second difference:
x 10 11 12 13 14
f(x) 50 71 94 119 146
1st diff 21 23 25 27
2nd diff 2 2 2
We got a constant second difference, so f is a polynomial of degree two.
Answer: This function is quadratic
