1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inverse of polynomial in dy^2 + ey + f form

  1. Sep 10, 2010 #1

    I'm trying to find the inverse polynomial of y = ax^2 + bx + c in the form of x = dy^2 + ey + f.

    I'm able to approximate this using Excel, but would prefer a more elegant solution. Any suggestions?

  2. jcsd
  3. Sep 10, 2010 #2
    Isolate x in terms of y using the quadratic formula should give you the inverse.
  4. Sep 10, 2010 #3


    User Avatar
    Homework Helper

    I don't think I'm understanding your problem properly because the inverse of [tex]y=ax^2+bx+c[/tex] IS [tex]x=ay^2+by+c[/tex] and so d=a, e=b, f=c
  5. Sep 10, 2010 #4
  6. Sep 10, 2010 #5
    Thanks for the replies, I apologize for not being more descriptive in my question.

    Gerenuk's reply is close to what I am looking for, although I think I may need to increase the terms - a quick set of data against the equation was off.
  7. Sep 11, 2010 #6


    User Avatar
    Science Advisor

    Mentallic is correct: the "inverse function" to [itex]y= ax^2+ bx+ c[/itex] is just [itex]x= ay^2+ by+ c[/itex]. Now use the quadratic formula to solve for y:
    [tex]y= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}[/tex]

    But notice the "[itex]\pm[/itex]". The quadratic function is not one-to-one and so does not have a true "inverse". You could restrict x to one side or the other of the vertex of the parabolic graph, thus using either the "+" or the "-".
  8. Sep 12, 2010 #7
    Neither of you is correct, because you don't understand the question. He might not have used the proper wording, but it's not hard to guess what he is really looking for.

    @SteveC: Maybe you want to look at Chebychev Polynomials and their Approximation theory. They provide a method to vaguely minimize the maximum total error. Whereas the series expansion I wrote down only aims to be best a y=0.
  9. Sep 13, 2010 #8


    User Avatar
    Homework Helper

    Yep, I already acknowledged that I might not be understanding it properly.

    The way he asked it, my answer is correct. I was only sceptical about my answer because it was too simple.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook