given the following table, develop the polynomial expression that defines the data. show all steps. you may verify using regression but the answer must be obtained using algebra.
x y
-2 -41
-1 -11
0 -3
1 -5
2 -5
3 9
4 49
5 127
6 255
I guess one way to do it would be to plot the data, or create a mental image of the graph.
Then, as it appears to be a cubic, you can sub in co-ordinates into the general cubic equation, then solve the simultaneous equations to get the unknowns.
You could then test this equation using the other x and y values.
Poorly posed question you could put a Lagrange interpolating polynomial through the data, which would go through every data point but in practice be useless.
CB
Another way to find the equation using algebra is to use finite differences:
Finite Difference -- from Wolfram MathWorld
It looks complicated at first, but it's actually pretty simple; though tedious.