Paired parabolas

Some parabolas are related to others. How are their equations and graphs connected?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative
Image
Powerful Quadratics


This resource is from Underground Mathematics.

 



What's the same and what's different about the following pairs of equations?

 

  1. $y=x^2-4$ and $y+x^2-4=0$

     
  2. $y=4-9x^2$ and $y+4=9x^2$

     
  3. $2y=4x^2-6$ and $-(y-3)=2x^2$



If you were given the following picture, could you suggest the equation of its pair?

 

 

 

 

Image
Paired parabolas

 



How about if you were given this picture instead?

Could you give the equation of its pair?

 

 

 

 

 

 

 

 

 

Image
Paired parabolas


 

 

 

 

 

 

 

This is an Underground Mathematics resource.

Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.

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