Answer:
B. The relationship between the variables in the table is quadratic because the second differences are constant.
Step-by-step 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.
