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Question

Notice that the third column lists the differences between successive y-values. Is there a pattern to the column of differences? Do the values in this column describe a linear function? Explain. As a check, create a fourth column that tables the differences of the differences. How does this column help you with your thinking?

___

x I y I diff I

0 I 0 I 1 I

1 I 1 I 3 I

2 I 4 I _ I

3 I 9 I _ I

4 I I _ I

5 I

Answer 1

Because the '2nd difference' is linear or1st degree, the function is quadratic or 2nd degree.

The next column would be all 2s. And the column after that all 0s.

Congratulations, you just had your first Calculus lesson!