1. data equation

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

2. Do you have Excel?. It does a find job of regressions.

I get a cubic that fits well. It has an R^2=1

$y=2x^{3}-5x^{2}+x-3$

3. 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.

4. Originally Posted by william
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
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

5. how would i do this using just algebra? can anyone get me started? and how do i write the equation of the family of quartic functions that have a zero at -3?

6. Originally Posted by william
[snip]
and how do i write the equation of the family of quartic functions that have a zero at -3?
The model for that type of quartic is $y = (x + 3)(ax^3 + bx^2 + cx + d)$.

7. 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.