Exploring the Parabola

What properties of the parabola can you deduce from this worksheet? What is the importance of the points A, B, C and D?

What happens if C does NOT lie at the midpoint of AB?

Move the point B to trace the locus of the parabola which has A as its focus and the x-axis as directrix.
Now use the three sliders to try and match the function to the curve.

Steve Arnold, 18/06/06, Created with GeoGebra

This problem may also be modelled using CabriJr on the TI-83/84 series calculator. Click on the graphic below to download the file and try it yourself!

Try having students work in pairs: one generating data points using the CabriJr model and the partner entering these into lists to plot and then to help build their algebraic model!

...And just wait until you try this with TI-nspire CAS!