Curves from Geometry

Escape to investigate hyperbolas. Pupils take a look at what happens to the elliptical orbital path of a satellite that exceeds escape velocity as the opener to the eighth lesson in a unit of 23. Scholars analyze basic hyperbolas and how the graph changes based on changes to the parameters in the equation. Using the changes, class members develop an understanding of how to graph a hyperbola simply by looking at the equation.

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CCSS: Designed
Additional Tags
Instructional Ideas
  • Create a graphic organizer showing the forms of the equations for circles, parabolas, ellipses, and hyperbolas
Classroom Considerations
  • Assumes learners are familiar with equations as a polynomial and in standard form of parabolas and ellipses
  • Requires the ability to complete the square
Pros
  • Includes a table to summarize properties of ellipses and hyperbolas
  • Contains answer keys for examples, the exit ticket, and exercises
Cons
  • None
Common Core