Create Quadratic equation for number of regions based on tabular info

[brooke01]

Number of tangents	Maximum number of separate regions
1	3
2	6
3	10
4	14
5	19
6	24
7	28
8	37

I need to create a quadratic equation that for the maximumnumber of separate regions by using this table. I cannot find a pattern and I haveno idea how to even start to work this out
Thanks

 

[Deleted member 4993]

Number of tangents	Maximum number of separate regions
1	3
2	6
3	10
4	14
5	19
6	24
7	28
8	37

I need to create a quadratic equation that for the maximum number of separate regions by using this table. I cannot find a pattern and I have no idea how to even start to work this out
Thanks

Are you allowed to use any commercial software like MS-excel?

 

[stapel]

Number of tangents	Max. number of sep. regions
1	3
2	6
3	10
4	14
5	19
6	24
7	28
8	37

I need to create a quadratic equation that for the maximum number of separate regions by using this table. I cannot find a pattern and I have no idea how to even start to work this out

Try using the method outlined here using, say, the first three or four data points. Then check your equation with some of the other data points.

Note: I get an equation from the first three data points that does not gibe with other points. Are you sure that you're supposed to be finding a quadratic equation? And what is meant by "tangents" in this context? Thank you!

 

[Ishuda]

Number of tangents	Maximum number of separate regions
1	3
2	6
3	10
4	14
5	19
6	24
7	28
8	37

I need to create a quadratic equation that for the maximumnumber of separate regions by using this table. I cannot find a pattern and I haveno idea how to even start to work this out
Thanks

(1) Assuming you want a quadratic fit to all the data I would note that if you graph the points, it is obvious that point 7 stands out as 'being out of line for a quadratic fit'. Thus, not having something like a quadratic least squares fit available to me, I would use the method indicated by stapel on say, the 1st, 4.5th (average of the 4th and 5th point assuming you want equal spaced data), and 8th point.

(2) Your "... for the maximumnumber of separate regions by using this table." confuses me. The curvature of the graph is upward indicating a quadratic fit with a minimum rather than a maximum so I would expect the statement to be something like "for the minimum number of separate regions."