Problem 5
Given two points (x
0,y
0) and (x
1,y
1), we can construct a function that passes through
them by solving the following system of equations:
a1x0 + a0 = y0
a1x1 + a0 = y1
for a
0 and a
1.
Simliarly for three points (x
0,y
0), (x
1,y
1), and (x
2,y
2) by solving
a2x02 + a1x0 + a0 = y0
a2x12 + a1x1 + a0 = y1
a2x22 + a1x2 + a0 = y2
for a
0, a
1, and a
2.
This process can be done with any number of points and is known as interpolation.
The resulting polynomial is called the interpolating polynomial.
Determine the interpolating polynomial that passes through the following points (1,1), (2,10), (3,6), (-1,-2).
Use the interpolating polynomial to determine f(0), f(-2), and f(-3).
Students, email your solutions to
atew@unomaha.edu.
Solutions are due by 11:59PM on Friday, October 15th, 2010.
Along with your solution, include your name, your school's name,
the name of your math teacher or math club moderator, and your year in school.
Don't forget to
send your work with your solution.
