Help needed, rearranging polynomial for inverse equation

[Charij]

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

 

[micromass]

Complete the square.

 

[Charij]

Great thanks!

That in mind I've got:

x = \frac{\sqrt{y - c - \frac{b^{2}}{4a}} - \frac{b}{2\sqrt{a}}}{\sqrt{a}}

 

[Vargo]

Check out the Wolfram Equation Solver:

http://www.wolframalpha.com/examples/EquationSolving.html

You would want to "solve an equation with parameters". Their answer looks a bit different, so you can look at their step by step breakdown and see whether your answer is equivalent.

 

[CompuChip]

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.

 

[HallsofIvy]

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.

 

[Charij]

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!

 

[CompuChip]

If you already have a square you can solve for p = (dx + e) first.