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Name That Graph

Age 16 to 18 Challenge Level:

This resource is from Underground Mathematics.

Take a look at the parabola below.

Can you find an equation for this parabola?


  • In how many ways can you choose to show this equation?
  • Which format did you initially choose and why?

What is the same and what is different about your approach to finding an equation of the two parabolas below, compared to the example above?











  • What properties do the three parabolas have in common?
  • Is there an approach to finding the equation that works for all three of these parabolas, and indeed for any parabola you could be given?
  • Which approach to finding the equation was the most efficient? Is it the same approach for each example?




This is an Underground Mathematics resource.

Underground Mathematics is funded by a grant from the UK Department for Education and provides free web-based resources that support the teaching and learning of post-16 mathematics. It started in 2012 as the Cambridge Mathematics Education Project (CMEP).

Visit the site at to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.