## Solving Quadratics

There are three ways in which you can solve quadratics – each method requires setting the quadratic to 0 first:

### Factorising

This is the simplest method provided that the quadratic can be factorised.

*Example*:

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### 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. See Discriminants page.

The quadratic formula says that if then the roots are given by:

### Completing the Square

This is another infallible method for finding roots if a quadratic can be solved. See Completing the Square page.

*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).

1. Find the roots using one of the above methods, roots occur when y=0.

2. Find the y-intercept, this occurs when x=0.

3. Find the coordinates of the vertex by completing the square and applying transformations to .

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