How to find an equation with multiple x,y coordinates

[beamthegreat]

Hi, I tried using geogebra to find an equation that exactly goes through the list of points I plotted on the graph but I failed to find any way so far. I have tried using, FitExp, FitGrowth, and Fitline, and so far none of them worked. I have no idea what kind of equation this is so I cannot used the Fit command. Any Ideas on how I can find the equation using Geogebra or any other method?

Here are the points:

10 - 54
20 - 216
30 - 486
40 - 864
50 - 1350
60 - 1944
70 - 2646
80 - 3456
90 - 4374

Thanks.

 

[Integrand]

Hi. The relationship between your data points is quadratic. Try searching for a tutorial on the method of common differences for sequences, it's very easy to apply and you'll get a nice neat equation.

Hint: In general you'd get an equation of the form y = ax² + bx + c, but with your data b = c = 0.

Also note: Now that I've told you it's quadratic, you could of course just ask your software for the solution. Don't cheat yourself! Use google to look into the method I mentioned above, and take the first step toward arming yourself to deal with such problems in the future.

 

[HallsofIvy]

More generally, there exist a unique n-1 degree polynomial that passes through any given n points so, at worst, an 8 degree polynomial could be fit to it.

 

[thelema418]

You could always use Excel for this. If you do not have that program, Google Docs Spreadsheet will probably suffice.

The best recommendation I can give is for Excel 2007 on a PC. I would enter the data into the spreadsheet, then highlight the data, and create a scatter-plot chart. Select the chart, and choose the Layout Tab from the Chart Tools category. There should be a button that says "Trendline". Choose "More Trendline Options".

Select Polynomial Order 2. There's also a check box for "Display Equation on Chart". That will give you the equation.

Note: you can look at other types of trendlines and polynomials to see what would be a best fit.

Another analysis you can do in Excel is to calculate the differences of the successive range values. Then calculate the differences of those differences. For you're data, I got:

10 54
20 216 162
30 486 270 108
40 864 378 108
50 1350 486 108
60 1944 594 108
70 2646 702 108
80 3456 810 108
90 4374 918 108

Note how the difference of the differences is 108 in every case. You can use this type of information to figure out the type of equation too.

 

[Redbelly98]

It's a lot easier if you can work with smaller numbers, which we can do in this case. The x values are all multiples of 10, so you might as well just use 1, 2, 3, ... 9 instead of 10, 20, etc. This is just easier to work with.

Also, the y values are all even numbers, so could obviously be divided by 2. Looking more carefully, they turn out to be divisible by 9 as well. So divide all the y values by 18. There might turn out to be yet more common factors to divide the y values down.

So the first two y values become 3 and 12 (54/18 and 216/18). Hmmm, wonder if there is another common factor of 3 here? If we divide all the y values by 3 and 18 -- in other words, divide them all by 54 -- then a very clear pattern becomes evident.