Generating equation for a parabola bundle

[PaulLag]

Hi there
Hope everybody is fine

Please I hope someone can help me in following topic.

I have a bunch of parabolic set of data, is to say
Abscissa data 1 … data n
x1 y1_1 … y1_n
x2 y2_1 … y2_n
x3 y3_1 … y3_n
x4 y4_1 … y4_n

x1, x2, x3, x4 is the same for each set of data.
each set of (abscissa, data), generate a parabola.
Y = a(1)x^2+b(1)x+c(1)
….
Y = a(n)x^2+b(n)x+c(n)
All these parabolas have one point in common
I’d like to find a way in order to summarize all these parabolas in a formula like this

Y = k(ax^2+bx+c)

Please is there a way to realize this regression in excel ?
The idea is to determine a,b,c and the value of k for each set of data.

Many thanks

[zbor]

Attach a sample workbook. Make sure there is just enough data to demonstrate your need. Include a BEFORE sheet and an AFTER sheet in the workbook if needed to show the process you're trying to complete or automate. Make sure your desired results are shown, mock them up manually if necessary.

Remember to desensitize the data.

Click on GO ADVANCED and use the paperclip icon to open the upload window.

View Pic

[MrShorty]

If you are unfamiliar with the =LINEST() function, you will almost certainly want to become familiar with this function: https://support.office.com/en-us/art...a-fa7abf772b6d

You will need to test to see if this will work, but if this Y = k(ax^2+bx+c) is your starting point, a very little algebra should show that y/k=ax^2+bx+c. Substitute u=y/k, if needed, and it should be obvious that a new regression equation of u=ax^2+bx+c. Then see where that leads you.