Question

Which kind of function best models the data in the table. Use differences or ratios.

x | y
-3 11.5
-2 7
-1 3.5
0 1
1 -.5
2 -1

(Linear, Quadratic, Exponential or None)

Answer 1

This is a quadratic relationship.

The first differences would be as follows:
11.5 - 7 = 4.5
7 - 3.5 = 3.5
3.5 - 1 = 2.5
1 - -0.5 = 1.5
-0.5 - - 1 = 0.5

Since they are not the same, it is not linear.

The second differences would be:
4.5 - 3.5 = 1
3.5 - 2.5 = 1
2.5 - 1.5 = 1
1.5 - 0.5 = 1

Since the second differences are the same, it is a quadratic relationship.