a.
To make: A table of second differences for given polynomial and make conjecture about the second differences.
x | y | First difference | Second difference |
-2 | 8 | -6 | 4 |
-1 | 2 | -2 | 4 |
0 | 0 | 2 | 4 |
1 | 2 | 6 | |
2 | 8 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
Given information:
Explanation:
Create a table to first list the first difference and then second.
x | y | First difference | Second difference |
-2 | 8 | -6 | 4 |
-1 | 2 | -2 | 4 |
0 | 0 | 2 | 4 |
1 | 2 | 6 | |
2 | 8 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
b.
To make: A table of second differences for given polynomial and make conjecture about the second differences.
x | y | First difference | Second difference |
-2 | 20 | -15 | 10 |
-1 | 5 | -5 | 10 |
0 | 0 | 5 | 10 |
1 | 5 | 15 | |
2 | 20 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
Given information:
Create a table to first list the first difference and then second.
x | y | First difference | Second difference |
-2 | 20 | -15 | 10 |
-1 | 5 | -5 | 10 |
0 | 0 | 5 | 10 |
1 | 5 | 15 | |
2 | 20 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
c.
To make: A table of second differences for given polynomial and make conjecture about the second differences.
x | y | First difference | Second difference |
-2 | 18 | -15 | 10 |
-1 | 3 | -5 | 10 |
0 | -2 | 5 | 10 |
1 | 3 | 15 | |
2 | 18 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
Given information:
Create a table to first list the first difference and then second.
x | y | First difference | Second difference |
-2 | 18 | -15 | 10 |
-1 | 3 | -5 | 10 |
0 | -2 | 5 | 10 |
1 | 3 | 15 | |
2 | 18 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
d.
To make: A table of second differences for given polynomial and make conjecture about the second differences.
x | y | First difference | Second difference |
-2 | 28 | -21 | 14 |
-1 | 7 | -7 | 14 |
0 | 0 | 7 | 14 |
1 | 7 | 21 | 14 |
2 | 28 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
Given information:
Create a table to first list the first difference and then second.
x | y | First difference | Second difference |
-2 | 28 | -21 | 14 |
-1 | 7 | -7 | 14 |
0 | 0 | 7 | 14 |
1 | 7 | 21 | |
2 | 28 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
e.
To make: A table of second differences for given polynomial and make conjecture about the second differences.
x | y | First difference | Second difference |
-2 | 29 | -21 | 14 |
-1 | 8 | -7 | 14 |
0 | 1 | 7 | 14 |
1 | 8 | 21 | |
2 | 29 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
Given information:
Create a table to first list the first difference and then second.
x | y | First difference | Second difference |
-2 | 29 | -21 | 14 |
-1 | 8 | -7 | 14 |
0 | 1 | 7 | 14 |
1 | 8 | 21 | |
2 | 29 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
f.
To make: A table of second differences for given polynomial and make conjecture about the second differences.
Create a table to first list the first difference and then second.
x | y | First difference | Second difference |
-2 | 23 | -18 | 14 |
-1 | 5 | -4 | 14 |
0 | 01 | 10 | 14 |
1 | 11 | 24 | |
2 | 35 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
Given information:
Create a table to first list the first difference and then second.
x | y | First difference | Second difference |
-2 | 23 | -18 | 14 |
-1 | 5 | -4 | 14 |
0 | 01 | 10 | 14 |
1 | 11 | 24 | |
2 | 35 |
The second difference is constant as the given polynomial is a quadratic polynomial with degree 2.
Chapter 5 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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