Quartic function in order to x (help pleaseee)

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skanpt

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Hello everyone! I have this function: y=0,0001x4- 0,0206x3 + 1,3824x2 - 38,464x + 626,43

I want to make this function looks like "x=something" and not "y=something" ...

How can I do that? Can anyone help me? That's the last step to finish my project :) Any help is appreciated! Thank you.
 
You can do that, but only locally - unless you are particularly lucky.

How did you obtain this equation? That information may lead to a simpler solution.
 
You CAN do this by applying the quartic formula, but will not get a unique function. You will get four different functions.

[MATH]y = ax^4 + bx^3 + cx^2 + dx + g \implies ax^4 + bx^3 + cx^2 + dx + e = 0, \text { where } e = g - y.[/MATH]
Now solve for x by applying the quartic formula, given here.


Be careful not to make any arithmetic errors.
 
Thank you for the responses. I'll try to explain the "problem":

I made a plot with some points on Excel and I made a trend line (quartic polynomial). The function presented is to the dotted line. But what I want is to make x=something.

13166
 
skanpt said:
Thank you for the responses. I'll try to explain the "problem":

I made a plot with some points on Excel and I made a trend line (quartic polynomial). The function presented is to the dotted line. But what I want is to make x=something.

View attachment 13166
Click to expand...
That's rather what I was guessing. Now, swap your x and y coordinates and do the same thing.
 
I already tried it, but I can't get a good trend line... I'll give you the point that I'm using, maybe I'm doing something wrong :/

X/Y values:
248 / 25
268 / 30
270 / 40
271 / 50
274 / 60
327 / 70
472 / 80
598 / 85
711 / 90

In the last graph, the values were inverted (The X is now the Y and vice versa). Can you put the values in your Excel? It gives me this graph:
13169
 
Yes. that looks right. What more do you want? "Making x the subject of the equation" is equivalent to "solving the equation for x". For this quartic equation that is very difficult.
 
First, in post #4, your quartic is probably not reliable. You have a small data set, just 9 points and, with a quartic, only 4 degrees of freedom. The coefficient on the quartic term is almost certainly too small to be statistically significant, and the coefficient on the cubic term may also be too small to be statistically significant. If you used Excel's data package, it provides an extensive list of statistics. What are they?

Second, using software is dangerous. It does what you tell it to do, but that does not mean you tell it to do makes any sense. You have not told us what x and y are. Just looking at the data, I am dubious that y is dependent on x. Even if it is plausible that y is dependent on x, why is it plausible that the dependency be in the form of a polynomial, let alone a quartic? Is it plausible that y is dependent on more than one variable?

Third, in post # 4, you got two graphs: one joining the data points and the other for your equation. In post 6, you did not do that? Why not?
 
Further, polynomials, in general, are very nice for following a dataset. Simply pick a high enough degree and you can at least imagine that you have done well. On the other hand, they DO NOT behave well outside your dataset.
 
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