Finding PolynomialsDate: 04/29/97 at 01:16:33 From: Elizabeth Subject: Algebra I - Find the polynomial I need to know what algebric equation fits the following data: x y -- -- 1 6 2 13 3 21 4 30 5 40 6 51 Thank you! Date: 04/29/97 at 15:03:47 From: Doctor Rob Subject: Re: Algebra I - Find the polynomial The usual way to work this kind of problem is to look at the difference of successive values of y: x: 1 2 3 4 5 6 y: 6 13 21 30 40 51 7 8 9 10 11 Next, find the differences of the differences: x: 1 2 3 4 5 6 y: 6 13 21 30 40 51 7 8 9 10 11 1 1 1 1 These are a constant (1), and so the equation is going to look like: y = a*x^2 + b*x + c (second degree) To find a, b, and c, use the first three (x,y) pairs: 6 = a*1^2 + b*1 + c = a + b + c 13 = a*2^2 + b*2 + c = 4*a + 2*b + c 21 = a*3^2 + b*3 + c = 9*a + 3*b + c Here you have three simultaneous equations in three unknowns a, b, and c. Subtract the second from the third, and the first from the second: 6 = a + b + c 7 = 3*a + b 8 = 5*a + b Now subtract the new second from the new third: 6 = a + b + c 7 = 3*a + b 1 = 2*a Now it is easy to figure out a from the last equation. Using that, figure out b from the previous one, and using both, figure out c from the one before that. Once you know a, b, and c, you know what y is as a polynomial in x. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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