Math and PHP - solved

[requinix]

I've got a graph, and I want to put a best-fit line to it. A quadratic best line - not linear.
I've seen a number of modules and functions that can find a y=mx+b equation, but not a y=ax^2+bx+c line.

Any suggestions on how I could do it myself? Or anywhere with a function to do it for me?

I'm thinking that eval() might come in handy...

Edit:
Whoops.

I have a set of data points (no more than 30). I want to find a quadratic best-fit for them, then graph it on the same picture.
I can do the graphing - I just need to find the right numbers first.

[Rayquazza]

Doesn't eval evaluate text as PHP code?If PHP can't do it, eval() can't do it >.>
You're trying to do a parabola, but are you trying to do a graphic, or just output numbers?

[requinix]

Yeah, but the point is it lets me put together a PHP string step by step, then it can be evaluated.
Anyways, the end result is a graph of it, but I can do that easily enough if I have the numbers.

[Rayquazza]

Something like this?
http://www.melchior.us/parabola.php

[requinix]

gonk I forgot to say the important bit...

Another edit:
I'll be back in a couple hours to check this...

[Wesker99]

How could there be a line of best fit for a parabola?

Are you talking about y = -2b/c for the center line?

[Rayquazza]

That's -b/2a if I'm not mistaken.
[-b(+-)sqrt(b^2-4.a.c)]/2a to get the places where it touches X axis (X1, X2)
(x1+x2)/2 OR -b/2a to get the Yv and replace Yv as the X in the ax^2+bx+c equation to get Xv.

[Wesker99]

same effect.. sometimes razz

[requinix]

Wesker99

How could there be a line of best fit for a parabola?

(Sorry about the late reply)
I want a method to find a quadratic equation that minimizes the difference between the calculated y given an x (what the equation would give) and the actual value of y (the data point).

I can find a simple way to calculate the linear equation, but I want a quadratic. And it has to be possible in PHP - that means no derivatives, no limits, and not even basic algebra.

It has to be possible: MS Excel can find them even to a fifth-order equation, and in very little time too.

[requinix]

Eh, that's how it goes...

I just tried searching for something slightly different than I've been trying, and now I have the solution. Without actually giving the solutions for a, b, and c (it's long sweatdrop ), it was this that "gave" me the answer (I still had to solve those last three equations).

Plus, the answer is so simple, I feel stupid for not figuring it out myself (behind computers, math is my best subject) redface