# acquiring a cubic equation from a data table

• Feb 22nd 2009, 12:17 PM
roloddt
acquiring a cubic equation from a data table
I'm not allowed to use a calculator on this one....
I have to get a cubic equation from a set of points but they don't have a constant D3.
I completely forget how to do this...
the set of data are: left is x right is y
• Feb 22nd 2009, 12:37 PM
HallsofIvy
Any cubic equation is of the form $y= Ax^3+ bx^2+ cx+ d$. One way to get a cubic equation from the data is to just pick three points and put their x and y values into that, so you have 3 equations to solve for a, b, and c. If I were doing this I would pick numbers at the beginning, center and end of the list.

Or you might be expected to give the "least squares" cubic approximation. That's much harder.
• Feb 22nd 2009, 12:42 PM
roloddt
Quote:

Originally Posted by HallsofIvy
Any cubic equation is of the form $y= Ax^3+ bx^2+ cx+ d$. One way to get a cubic equation from the data is to just pick three points and put their x and y values into that, so you have 3 equations to solve for a, b, and c. If I were doing this I would pick numbers at the beginning, center and end of the list.

Or you might be expected to give the "least squares" cubic approximation. That's much harder.

I forget how to do that....sorry~
but could you show me how to do it? just for like 2 equations and I'll be able to catch on.