Modelling Quadratics

Find curves in monuments, buildings and water jets and fit a parabola to them using dynamic geometry software.' 

Quadratic graphs are everywhere you look.  They can describe the paths of rockets, balls and jets of water.  Because of their symmetry you will see parabolas in bridges, buildings, sand dunes...  Understanding their equations is hence hugely important in the fields of engineering and science.  This activity uses dynamic geometry software to help students understand the graph of  quadratics in the form y = a(x - b)² + c.

Watch this screencast to see the activity in action:


  • Find below 3 GeoGebra files with some beautiful images.
  • If you are using Internet Explorer you may experience some difficulties viewing the applets below. If that is the case try these direct links to the applets

Eiffel Tower          Centennial Fountain          Art Museum in Valencia


  • Can you find the equations of the parabolas in the photographs above?
  • Students will need access to a computer to complete this activity.
  • Three dynamic geometry files are included for students to play with.
  • Use the Geogebra applets and use the sliders to change the values of the parameters a, b & c to get a best fit to the parabola curve.
  • What do a, b and c tell you about the graph? Why?
  • Students may wish to use their own images which can be found here
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