This applet uses some nice features of Geogebra 4 (including multivariable functions) to create an interactive worksheet that can be used to investigate how many normals to [math]y=x^2[/math] go through a specified point.
The general question involves generating and solving a cubic, but with care students can investigate sub-problems that only involve solving quadratics. As an investigation it is suitable for an advanced A-level class.
