Question

1. Use successive differences to classify the function represented in the table. Here is the table:

I'm stumped on how to do this.
Any help would be appreciated!


x 0 1 2
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14 5 2 5 14

Answer:

Answer 1

We see that the differences are -9, -3, +3, and +9.  Thus, we see that the function is symmetric about x=2 (I'm assuming the five values correspond to x=0, 1, 2, 3, 4) and increases at a rate similar to (x-2) squared.  With that in mind, we classify this function as a parabola, as the standard form of a parabola (y=a(x-h)^2 + k) shows similar growth to this function.