x | y | first difference | second difference
1 | 4 | |
2 | 10 | 6 = 10 - 4 |
3 | 18 | 8 = 18 - 10 | 2 = 8 - 6
4 | 28 | 10 = 28 - 18 | 2 = 10 - 8
5 | 40 | 12 = 40 - 28 | 2 = 12 - 10
Given that the first differences are not equal, then the equation is not a line
Given that the second differences are equal, then the equation is a quadratic function.
Therefore, the function can be modeled by the next equation:
where a, b, and c are some coefficients.
With the help of software, we get:
Rounding c to zero, the obtained equation is:
