NAME:________________________________________
DATE:__________
Discovery Algebra 2 – Successive Differences of Polynomials and solving systems of equations in three
variables
PART I: Successive Differences of Polynomials

How can finding a pattern of differences help determine what type of function is represented?
1) LINEAR FUNCTION:
x
y
-2
-8
-1
-3
0
2
1
7
2
12
x
y
1
2
2
5
3
6
4
5
5
2
2) QUADRATIC FUNCTION:
3) CUBIC FUNCTION:
x
y
0
2
1
1
2
6
3
23
4
58
5
117
LOCATION OF REGRESSION IN THE CALCULATOR


Enter the data into the calculator under STAT  EDIT. (L1 = x-values and L2 = y-values)
Your regression options can be found under STAT  CALC (scroll for more choices)
Linear
Quadratic
Cubic
Example 1: What type of relationship is indicated by the following set of ordered pairs? Explain how you
know. Then find the equation that satisfies the set ordered pairs.
X
0
1
2
3
4
5
Y
3
5
13
33
71
133
Example 2: 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.
Then use this equation to find y when x = 6.
X
0
1
2
3
4
5
Y
24
6
0
6
24
54
PART II: Solving System of Equations with 3-variables
1) Solve the following systems of equations.
2)