### Home > APCALC > Chapter 1 > Lesson 1.3.3 > Problem 1-128

While studying the finite differences of a particular function, Neo noticed that the differences changed linearly. What can you tell him about the original function? Also, how do his finite differences change? Homework Help ✎

A linear changing difference is a difference that increases or decreases in greater amounts each time. For example, if *f*(1) = 1, *f*(2) = 4, *f*(3) = 9, *f*(4) = 16, then the differences are 3, 5 and 7, respectively, and changing linearly, in this case with the linear rule, 2*x* + 1. What kind of function has this kind of change?

The original function is quadratic.

Take a quadratic function and list out some successive differences. For example, let's take the differences from the earlier hint: 3, 5, and 7. What is the difference between these differences and how do they change? If they don't change, what is the term for that?

The differences of the differences are constant.