Question

Tell whether this function is quadratic. {(10, 50), (11, 71), (12, 94), (13, 119), (14, 146)} .

Answer 1

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