Tom claims that, because the data pairs (1, 4), (2, 6), (3, 9), and (4, 13.5) have y-values with a common ratio, the are best modeled by a quadratic function? what is his error?

In order to validate Tom's claim, we have to calculate if indeed there is a common ratio with the consecutive y-values in the given ordered pairs.
          1st and 2nd:      r = 6/4 = 1.5
           2nd and 3rd:     r = 9/6 = 1.5
           3rd and 4th:       r = 13.5 /9 = 1.5

We have validated the existence of a common ratio. However this does not conclude that the function is quadratic because the ratio between the values is in first order. 

It is going to be the third choice

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