Question 661813: If I am given 5 points how do I determine the polynomial equation? These are my given points
(-4,89), (-3,7), (-1,-1), (1,-1),(4,329) Answer by solver91311(24713) (Show Source):
There are a couple of ways to go about this. The easy way is to plug your points into a graphing calculator or a graphing program on your computer and let the computer figure it out.
The hard way is as follows.
Five points uniquely determine a 4th degree polynomial equation. The general form of a 4th degree polynomial function is:
Start with your first point and substitute the values:
Simplify:
Similarly, using the other points produce:
Then use whatever method you like to solve the 5X5 system of equations to determine your coefficients for the polynomial function. Hint: Multiply the third equation by -1, then add the third and 4th equations. The whole thing will reduce to . Go back and substitute for in the first 4 equations giving yourself a much simpler 4X4 system to solve.
John
My calculator said it, I believe it, that settles it
