I have a graph that is plotted by points: My graph
How can I find out which polynomial will fit my requirements? My goal: I have a graph of y (x) (I have provided its points in the link). And I need to plot the graphs c1 * f (n), c2 * f (n) so that the graph y (x) lies between them with a minimum deviation.
Moreover, c1 = 1, c2 = 2.
For example, I picked up a polynomial like this: 17x ^ 2-34x + 17
Did I do it right? Or which polynomial is right for me?
c1f(n)<=y(x)<=c2f(n)
I graphed the points in a spreadsheet and asked for the best fitting quadratic polynomial. The equation is $$ f(x) = 34.36x^2 - 571.09x + 2312.59. $$
That minimizes the difference between the curve and your data points in a particular way that's common in this kind of situation. It is a very good fit.
If you really need the inequalities you ask for you could play with the coefficients of that polynomial to guarantee them, but there is no standard mathematical way to get the "best" answer to the question as you have asked it.