Session 7, Part D: Quadratic Functions (25 minutes)
In This Part: Quadratic Functions and Differences | Summary
You know that for linear functions, the difference between successive outputs is a constant. For exponential functions, the ratio between successive outputs is a constant. Is there some similar pattern for quadratic functions? The next few problems will help you decide. Note 12
As described at the end of Part C, quadratic functions involve squaring an input. The simplest quadratic function is simply output = (input)2. Here's the start of a table for this function, with three columns: input, output, and the difference between successive outputs:
Video Segment This video segment shows how to create a table of first differences and second differences in the equation y = x2. Watch this segment after you've completed Problem D2. If you get stuck on the problem, you can watch the video segment to help you.
You can find this segment on the session video, approximately 15 minutes and 42 seconds after the Annenberg Media logo.
In Part C, you built a table for triangular numbers. One way to write the rule for triangular numbers is
output = (n2 + n) / 2.
Create a table for this rule for triangular numbers, and look for patterns in the first and second differences.