If you have studied Maths up to GCSE level then it is likely that you will have encountered a method of solving any quadratic equation (an equation of the form ax² + bx + c = 0) using the quadratic formula.
This formula is used to find where the quadratic equation crosses the x-axis (this is at y = 0). Although you have encountered this formula at GCSE it is unlikely that you will have encountered the proof as to why the formula works, which is a shame as it ties in some other GCSE Maths nicely and is in no way complex.
To solve ax² + bx + c = 0 for x you begin by
completing the square, rearrange and find what x equals, simple!
And there it is, the quadratic formula! As you can see, it really isn't very difficult to derive the formula and it is a great shame that teachers do not take to the time to show students why the formula works rather than just letting them blindly accept it.
