# Quadratics

## Solving Quadratics

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*–

## Sketching Quadratics

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).

### Solomon Practice Questions

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