Concept Byte: Identifying Quadratic Data

For Use With Lesson 4-3

You can identify perfect quadratic data when x-values are evenly spaced using the pattern in the differences between y-values.

Example

Image Long Description

For linear data, the first differences of adjacent y-values are constant. For quadratic data, the second differences are constant.

Exercises

Determine if each data set represents perfect quadratic data.

1. x	y
   − 2 negative 2	− 5 negative 5
   − 1 negative 1	0
   0	5
   1	10
   2	15

2. x	y
   1	6
   2	12
   3	22
   4	36
   5	54
   6	76
   7	102

3. x	y
   − 2 negative 2	− 8 negative 8
   − 1 negative 1	− 1 negative 1
   0	0
   1	1
   2	8
   3	27
   4	64

4. x	y
   − 3 negative 3	− 1 negative 1
   − 2.5 negative 2.5	− 3.75 negative , 3.75
   − 2 negative 2	− 6 negative 6
   − 1.5 negative 1.5	− 7.75 negative , 7.75
   − 1 negative 1	− 9 negative 9

5. x	y
   − 3 negative 3	− 13 negative 13
   − 1 negative 1	− 8 negative 8
   1	− 5 negative 5
   3	− 4 negative 4
   5	− 5 negative 5

6. Reasoning Can you use the method above to determine if a data set represents perfect linear or quadratic data if the x-values are not evenly spaced? Explain.

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