Question

Consider the table of values.

x y
-2 0
-1 2
0 6
1 12
2 20
3 30
4 42

Select the statement that is true about the table.

A.
The relationship between the variables in the table is linear because the first differences are constant.
B.
The relationship between the variables in the table is quadratic because the second differences are constant.
C.
The relationship between the variables in the table is linear because the second differences are constant.
D.
The relationship between the variables in the table is quadratic because the first differences are constant.

Answer 1

B. The relationship between the variables in the table is quadratic because the second differences are constant.

Explanation:

We have to look for the differences in the y values of the given table.

The y values are:

0, 2, 6, 12, 20, 30, 42

The differences between the consecutive values are:

2, 4, 6, 8, 10, 12

These are the first differences and are not constant. This means the relationship is not linear. Now we again find the differences between the consecutive values:

2, 2, 2, 2, 2

These are the second differences. The second differences are constant. So this means the given relationship is quadratic.

Therefore, option B gives the correct answer. The relationship between the variables in the table is quadratic because the second differences are constant.