There are three ways in which you can solve quadratics – each method requires setting the quadratic to 0 first:
By factorising – this is the simplest method provided that the quadratic can be factorised. Example: .
Using the quadratic formula – if a quadratic cannot be factorised but does have roots, then the quadratic formula will find them. Recall that the discriminant will tell you how many roots a quadratic has.
The quadratic formula says that if then the roots are given by .
Completing the square – completing the square this is another infallible method for finding roots if a quadratic can be solved. Example –
Completing the square is also useful for sketching a quadratic. The reason for this is that, by writing the quadratic in completed square form, we can see the transformations applied to the graph of . For example, is the graph of shifted to the left by 3 (x transformation) and then up by 1 (y transformation).