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!

Help needed, rearranging polynomial for inverse equation

  1. Mar 3, 2013 #1
    Hi, I need to rearrange an equation:

    y = ax^2 + bx + c

    to the form of:

    x = ?

    I'm not entirely sure how to go about this and the examples I've found require the equation to be in a different form. Any tips or a point in the right direction would be great!

    Thanks in advance
  2. jcsd
  3. Mar 3, 2013 #2
    Complete the square.
  4. Mar 3, 2013 #3
    Great thanks!

    That in mind I've got:

    x = [itex]\frac{\sqrt{y - c - \frac{b^{2}}{4a}} - \frac{b}{2\sqrt{a}}}{\sqrt{a}}[/itex]
  5. Mar 4, 2013 #4
  6. Mar 4, 2013 #5


    User Avatar
    Science Advisor
    Homework Helper

    Do you know the quadratic formula, which is the default solution of ax² + bx + c = 0? Or is that what you are trying to prove here? Because if not, you can pull y to the other side of the equals sign and apply the quadratic formula.
  7. Mar 4, 2013 #6


    User Avatar
    Science Advisor

    Complete the square or use the quadratic formula.

    Most people learn how to solve quadratic equations before they learn about "inverse functions". Also, at some point you will have a "plus or minus". Unless your domain is restricted, a quadratic function will NOT have an inverse function.
  8. Mar 4, 2013 #7
    I'm actually writing a program that works out a, b and c, but then needs to work out x given y. I probably used the wrong terminology to describe something along the way ^^

    The answer I first wrote was generated by getting the equation in the form of:

    y = (dx + e)^2 + f

    and then working out d, e and f. The wolfram example is much nicer solution though, and more efficient computer wise :)

    Thanks a lot for the help!
  9. Mar 5, 2013 #8


    User Avatar
    Science Advisor
    Homework Helper

    If you already have a square you can solve for p = (dx + e) first.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook