How do the consecutive terms relate to each other?
Quadratic
Practice makes perfect
We want to identify which kind of model best describes the data: linear, quadratic, or exponential. To do so we will calculate the difference between consecutive terms.
x
0
1
2
3
4
y
5
8
17
32
53
Let's begin with calculating the first differences.
The first differences are not all equal. Therefore, the table of values does not represent a linear function. Let's find the second differences and compare them.
Since the second differences are all equal, the table of values represents a quadratic function.
