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 ifthen 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
SolomonQuadraticQuestions
Open Solomon Practice Questions on Quadratic Formula in New Window
Open Solomon Quadratic Formula Solutions in New Window
Open more Solomon Quadratic Practice Questions in New Window
Open more Solomon Quadratic Solutions in New Window
Open Solomon Practice Questions on Factorising in New Window
Open Solomon Factorising Solutions in New Window