## Use of graphing tools for families of curves

The MEI specification includes guidance for activities that should be carried out during the course. The first, and possibly most important, of these is:"Graphing tools: Learners should use graphing software to investigate the

relationships between graphical and algebraic representations, e.g. understanding the effect of changing the parameter

*k*in the graphs of

*y*= 1/

*x*+

*k*or

*y*=

*x*² –

*kx "*

The ability to plot a family of curves, and observe the effect on the graphs of dynamically changing a parameter, is an incredibly powerful tool in helping students understand mathematical relationships. Understanding how a mathematical object changes is greatly enhanced by considering how its graphical representation moves.

## An example from the sample assessment materials

The sample assessment materials include the following question:Determine the values of k for which part of the graph of

*y*=

*x*² –

*kx*+ 2

*k*appears below the

*x*-axis.

Plotting this in GeoGebra gives the option to vary

*k*to see how the curve changes.

This immediately gives some insights into what is happening:

- How the graph changes for different values of
*k* - The graph is sometimes above the
*y*-axis for all values of*x* - For many values of
*k*the graph will be below the*x*-axis between two values of*x*

Using the software does not answer the question for the students but it does give them a picture which they can use to understand what the question in asking them. I think this is Ofqual's intention with their statement that the use of graphing tools should permeate the study of A level Maths - these tools are easily accessible for all students and can have a massive positive impact on the way they build their understanding of mathematical objects.