Question: 15 of 30:
The distance versus time plot for a particular object shows a quadratic relationship. Which column of distance data is possible for this situation?
Time (s) A. Distance (m) B. Distance (m) C. Distance (m) D. Distance (m) E. Distance (m)
0 0 2.00 9.00 ��‡ ��‡
1 1.00 4.00 18.00 1.00 1.00
2 4.00 6.00 27.00 0.50 0.25
3 9.00 8.00 36.00 0.33 0.11
4 16.00 10.00 45.00 0.25 0.06
5 25.00 12.00 54.00 0.20 0.04
6 36.00 14.00 63.00 0.16 0.02
To determine which column of distance data is possible for a quadratic relationship, we need to look for a pattern in the data that follows a quadratic function.
In a quadratic relationship, the distance (or y-values) will increase at a non-linear rate as the time (or x-values) increases. This means that the rate of change of the distance with respect to time is not constant but changing.
Let's analyze the data to see which column fits this pattern:
- In column A, the distance values increase linearly (2, 4, 6, 8, 10, 12). This does not follow a quadratic pattern.
- In column B, the distance values increase quadratically (9, 18, 27, 36, 45, 54). This fits the pattern of a quadratic relationship.
- In column C, the distance values increase exponentially (1, 1.00, 0.50, 0.33, 0.25, 0.20). This does not follow a quadratic pattern.
- In column D, the distance values decrease with a non-linear rate (��‡, 1.00, 0.50, 0.33, 0.25, 0.20). This does not follow a quadratic pattern.
- In column E, the distance values decrease exponentially (��‡, 1.00, 0.25, 0.11, 0.06, 0.04). This does not follow a quadratic pattern.
Therefore, column B is the correct column that represents a quadratic relationship.