# Thread: Determining Formula for a graph

1. ## Determining Formula for a graph

Can anyone please show me how to determine the formula of the plot dots in the graph, the dots I think is divided into three parts, I put a line between the parts to avoid confusion....

A looks something like a x^3 graph
B looks like a sine curve
C looks weird.....

Thanks in advance, the files are attached

2. Count the number of points in each graph. The polynomial that fits exactly will be of order one less than the number of points. Then you can set up a series of equations to solve simultaneously.

3. Originally Posted by Prove It
Count the number of points in each graph. The polynomial that fits exactly will be of order one less than the number of points. Then you can set up a series of equations to solve simultaneously.
Thanks,
sorry but I have a question, if you don't mind....
so one less than the number of points... the division A in the graph has 9 points, 9-1=8, so what now?

4. There are 9 points so you can fit a unique 8th degree polynomial through those nine points. One way to do that is what Prove It suggested: $\displaystyle y= ax^8+ bx^7+ cx^6+ dx^5+ ex^4+ fx^3+ gx^2+ hx+ i$. Putting the x and y values of the 9 points into that gives 9 equations to solve for the 9 numbers a, b, c, d, e, f, g, h, and i.

5. Originally Posted by HallsofIvy
There are 9 points so you can fit a unique 8th degree polynomial through those nine points. One way to do that is what Prove It suggested: $\displaystyle y= ax^8+ bx^7+ cx^6+ dx^5+ ex^4+ fx^3+ gx^2+ hx+ i$. Putting the x and y values of the 9 points into that gives 9 equations to solve for the 9 numbers a, b, c, d, e, f, g, h, and i.
o_0 this is gonna take a long long time.... I'll keep you guys updated if it worked or not :-)

6. Originally Posted by HallsofIvy
There are 9 points so you can fit a unique 8th degree polynomial through those nine points. One way to do that is what Prove It suggested: $\displaystyle y= ax^8+ bx^7+ cx^6+ dx^5+ ex^4+ fx^3+ gx^2+ hx+ i$. Putting the x and y values of the 9 points into that gives 9 equations to solve for the 9 numbers a, b, c, d, e, f, g, h, and i.
o_0 this is gonna take a long long time.... I'll keep you guys updated if it worked or not :-)

7. Okay so now I got 9 very long equations, I would use simultaneous equations... but I don't know where to start! any suggestions? thanks

8. Originally Posted by Ackbeet
I reached the limit before even finishing the second formula :-(

9. Hmm. What software is available to you? Mathematica? MATLAB? Maple? Excel? I think all of these packages could solve a 9 x 9 system of linear equations for you. I think even my TI-85 calculator could do that, though I grant you that it would be exceptionally laborious to do by hand.

10. ## Solving polynomial simultaneous equations

I have a very many (nine to be precise) simultaneous equations, I want to solve them to get a,b,c,d,e,f,g,h and i. I tried everything from websites to trying myself, but couldn't :-(

it is attached if you want to see it, please if anyone has a method of finding these values let me know....

11. Otherwise, write down your augmented matrix and upper triangularise the system using row operations yourself.

12. Originally Posted by Prove It
Otherwise, write down your augmented matrix and upper triangularise the system using row operations yourself.
You say it like its so simple, but I don't get a simple word!.... lol
but thanks for the throught :-)

13. Originally Posted by IBstudent
You say it like its so simple, but I don't get a simple word!.... lol
but thanks for the throught :-)
Then look them up and consider it a learning experience

14. The following commands in Mathematica solved the system:

f[x_]:= Aye x^8 + Bee x^7 + Cee x^6 + Dee x^5 + Eee x^4 + Eff x^3 + Gee x^2 + H x + Eye;
Solve[{f[2] == 426.8, f[3] == 470.2, f[4] == 503.4, f[5] == 557.3, f[6] == 564.7, f[7] == 575.4, f[8] == 579.8, f[9] == 624.7, f[10] == 669.9}, {Aye, Bee, Cee, Dee, Eee, Eff, Gee, H, Eye}]

It did claim that the coefficient matrix was badly conditioned. You might be better off plugging in different values for x, unless you don't have any control over where you sample your function.

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