# Math Help - acquiring a cubic equation from a data table

1. ## 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

2. 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.

3. 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.