NAME: ______________________________________________
DATE: __________________
Algebra 2: Lesson 5-1 Successive Differences in Polynomials
Learning Goals
1) How can we determine what type of a function a given set of points is represented by?
2) How can we determine the equation for a given set of points?
Linear Functions
x
0
y = 2x + 3
First Differences
1
2
3
4
5

What do you notice?
Let’s generalize this…
a
0
ax + b
b
1
a+b
2
2a + b
3
3a + b
First Differences
For a linear function the first difference is equivalent to _________
Quadratic Functions
Number
1
Square
First Differences
Second Differences
First Differences
Second Differences
2
3
4
5
6

What do you notice?
Let’s generalize this…
x
0
ax2 + bx + c
c
1
a+b+c
2
4a + 2b + c
3
9a + 3b + c
4
16a + 4b + c
For a quadratic function the second difference is equivalent to _________.
What do you think will happen if we have a cubic function?
Cubic Functions
x
0
ax3 + bx2 + cx + d
d
1
a+b+c+d
2
8a + 4b + 2c + d
3
27a + 9b + 3c + d
4
64a + 16b + 4c + d
First Difference
Second Difference
Third Difference
For a cubic function the third difference is equivalent to _________.
Example 1:
What type of relationship does the set of ordered pairs (x, y) satisfy? How do you know?
x
0
y
2
1
1
2
6
3
23
4
58
5
117
First Difference
Second Difference
Third Difference
Fourth Difference
Example 2:
What type of relationship is indicated by the following set of ordered pairs? Explain how you know.
Find an equation that all ordered pairs above satisfy.
Example 3:
Create a table to find the second differences for the polynomial 36 – 16t2 for integer values of t from 0
to 5.
x
0
1
2
3
4
5
Y
First Differences
Second Differences
Example 4:
Show that the set of ordered pairs (x, y) in the table below satisfied a quadratic relationship. Find the
equation of the form
that all of the ordered pairs satisfy.