Show that the following data can be modeled by a quadratic f

Show that the following data can be modeled by a quadratic function. Compute the first-order and second-order differences. Are second-order differences constant? Yes No

Solution

X                          0           1          2            3              4

P(X)                       6           5          6            9              14

I^st order difference         -1          1          3             5           

II^nd order difference             2          2           2                      

Here the second order difference is constant . Hence the given data can be modelled in quadratic fuction