First Differences

First and Second Differences.

How to find whether an equation has a relationship of linear, quadratic, or in some cases neither by the use of table of values.

A base quadratic equation used here is: y= x^2

In order to calculate the "First Differences", you need to subtract the second y value from first y value and then you continue the same with other y values. If the differences are constant, it means that the pattern is linear relationship. Its a must that all your x values are in order. If the first differences are not constant you can easily find the difference by find the difference by subtracting the second first difference from first value and if the difference is constant, the relationship is quadratic. However, if the first and second differences are not constant it is neither.

Recall :

Linear relationships have equal FIRST DIFFERENCES.
Quadratics relationships have equal SECOND DIFFERENCES.
If the FIRST or SECOND DIFFERENCES are not constant, it is neither.