tuning a parabola, or other polynomial, for a specific outcome

[LMHmedchem]

Hello,

 

I have some data,

(x,y)

(2, 0.356)

(3, 0.543)

(4, 0.724)

(5, 0.905)

(6, 1.086)

(7, 1.267)

(8, 1.448)

(9, 1.629)

(10, 1.810)

(11, 1.991)

(12, 2.188)

(13, 2.364)

 

the x,y plot is linear and the correlation R is 1.

 

The y value is a coefficient and I would like to non-linearize the coefficioent to create the following conditions;

when x=2, y=1

when x=13, y=2

when x=7, y=4

 

If I apply a parabolic transformation

 

y= A*(x^2) + (B*x) + C

 

with,

A = -2.42

B = 7.1

C = -1.222

 

I get close, but the maximum values is at x = 8, y= 3.985

 

This is the transformed x,y data

(x,y)

((2, 1.0)

(3, 1.920)

(4, 2.650)

(5, 3.222)

(6, 3.635)

(7, 3.889)

(8, 3.985)

(9, 3.922)

(10, 3.700)

(11, 3.320)

(12, 2.729)

(13, 2.040)

 

I need to shift the relative maximum of the parabola to be at x=7.

 

What I have so far was done by trial and error, but there must be atheorem that would allow me to solve for the correct polynomial andback engineer a solution.

 

I have attached an excel spreadsheet with the data and plots in case that helps.

 

Please feel free to move this post if I have put it in the wrong forum and thanks in advance for any help you can give.

 

LMHmedchem

distance-ratios_post_11-07-12.zip

Edited July 12, 2011 by LMHmedchem

[khaled]

I'm not good at this, but my guess is that if you want to limit it at 7,

 

max: X = 7 and Y = f(X) = f(7), where f(x) is the equation you use ...

 

correct me if i'm wrong,