Select and interpret a function model
The input is position index, measured in units, and the output is displacement, measured in m. The data describe this situation: a signed displacement is recorded around a reference position
The following exact data are used over the interval \(x\in\left[-6,6\right]\)
| position index (units) | displacement (m) |
|---|---|
| \(-6\) | \(-335\) |
| \(-3\) | \(-56\) |
| \(0\) | \(7\) |
| \(3\) | \(16\) |
| \(6\) | \(133\) |
The input values are equally spaced. The third differences of the outputs are \(162,;162\)
Which family gives a plausible model for all of the listed values?