In what useful ways can you rearrange a quadratic equation?
- Factorisation: x2 - 5x + 6 = (x - 2)(x - 3) This method is the quickest to perform if the roots are simple but does rely on a bit of trial and error. The method lets you find the roots of a quadratic equation. That is, the points at which the line crosses the x-axis.2) Quadratic Formula: x = (b +/- sqrt(b2 - 4ac))/2a This method is the go to if factorisation was not possible. A point to note is when are there no roots and what does the corresponding graph look like. Something that may be explored is how to actually derive this formula. This is something that I was never told but had to work on by myself but I think these sorts of questions are very important to doing well in maths.3) Completing the square x2 - 4x + 6 = (x - 2)2+ 2 This method allows us to find the point that is either the maximum or minimum of the parabola. In this case it is (2, 2) and a minimum. It is good for the student to understand why we can get the stationary point from this expression and not just perform it. This is also the starting point of deriving the quadratic formula.
