Aim 46: How do we use successive differences to determine the type of equation and to write an equation? Do Now: Consider the sequence {3, 5, 7, 9, 11, 13} What is the pattern?
1) Linear Functions
What do you notice? __________________________________________
Cube the terms in the original sequence, and then fill in the rest of the table below. For a linear function, the first difference is equal to 2) Quadratic Function
What do you notice? __________________________________________
For a quadratic function, the second difference is equal to _______.
What do you think will happen if we have a cubic function? Example 5 What type of relationship does the set of ordered pairs (x, y) satisfy? How do you know? Fill in the blanks in the table below to help you decide. (The first differences have already been computed for you.)
Find a polynomial function to model this data (you may use regression on the calculator)
Sum it Up
• Sequences whose first differences are constant satisfy a linear relationship.
• Sequences whose second differences are constant satisfy a quadratic relationship.
• Sequences whose third differences are constant satisfy a cubic relationship.
Homework #46­ Successive Differences Name ______________________
Algebra 2 Common Core
Date: ______________________
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