Question

Determine which parent function would best model the given data set.

Show your work by copying the table, showing 1st and, possibly 2nd, differences and/or ratios as
discussed and modeled in class.
Organize your work as mentioned in the course syllabus.
X1
O linear
2
4
6
8
10
12
quadratic
none of these
O exponential
V₁
84
72
52
24
-12
-56

Answer 1

To determine which parent function would best model the given data set, let's analyze the table and look for patterns.

X | V₁

----|-----

1 | 84

2 | 72

4 | 52

6 | 24

8 | -12

10 | -56

First, let's find the differences between consecutive values of V₁:

- The difference between 84 and 72 is -12.

- The difference between 72 and 52 is -20.

- The difference between 52 and 24 is -28.

- The difference between 24 and -12 is -36.

- The difference between -12 and -56 is -44.

Now, let's find the differences between these differences:

- The difference between -12 and -20 is 8.

- The difference between -20 and -28 is 8.

- The difference between -28 and -36 is 8.

- The difference between -36 and -44 is 8.

Since the second differences are constant and equal to 8, we can conclude that the data set is best modeled by a quadratic parent function.

Therefore, the correct answer is quadratic.

Explanation: