The distance versus time plot for a particular object shows a quadratic relationship. Which column of distance data is possible for this situation?

Quadratic relation ship is of the kind y = a (x-h) ^2 + k or y = Ax^2 + Bx + C

Where x is the time and y is the distance.

Then if you have the numbers ordered in a colum it must be true that:

x = 0 = > y = (0-h) ^2 + k = h^2 + k

x = 1 = > y = (1-h) ^2 + k = 1 - 2h + h^2 + k

x = 2 = > y = (2-h) ^2 + k = 4 - 4h + h^2 + k

x = 3=> y = (3-h) ^2 + k = 9 - 6h + h^2 + k

x = 4 = > y = (4-h) ^2 + k = 16 - 8h + h^2 + k

A particular case of this is when h = 0 and k = 0 (i. e. the vertex of the function is at (0,0)

For this case you will observe these numbers in the respective column:

x y

0 0

1 1

2 4

3 9

4 16

Then, if you have that column among the answers (which I am sure is the case) that is the right answer.