SOLUTION: 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)

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): You can put this solution on YOUR website!

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

The Out Campaign: Scarlet Letter of Atheism

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