How do I find the equation using the table of values ?

Question

Using the table of values given, determine the equation of the function that would model this data. show all workings

x    f(x)

1    0

2    3

3    16

4    45

5    96

6    175

 

how do I do this kind question, possibly using system of equations

Answer 1

how do I do this questions?      how do I do this kind of question? ⇐edited for correct grammar.

 

you plot (graph) the data and then use your judgment to decide what kind of curve fitting (regression) should be done, using a 'graphing calculator'.  Possible curve fitting regression options would be polynomial (degree 2 or more) or exponential.  The fit having the lowest value of r² is chosen by you as the best fit.