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Episode 6 Supports

  • Making Sense: Sasha and Keoni build on what they have learned in the previous episodes to begin to develop the general equation for any parabola with vertex (h, k) and the distance p from the vertex to the focus.

  • Sasha found the distance from the focus and the x-axis, which is k+p [1:59].  But she then equated this distance to the focus rather than identifying the coordinate pair that represents the focus.

     

    • After the teacher asks whether k+p represents the x-value or the y-value of the focus, Sasha and Keoni represented the focus with a coordinate pair [2:27].

  • For use in a classroom, pause the video and ask these questions:

     

    1. [Pause the video at 1:34]. Where is the length k on the graph?

     

    2. [Pause the video at 4:18]. What distance are Sasha and Keoni trying to find here? What is its significance?

     

    3. [Pause the video at 7:25]. How can you represent the length that Sasha just circled?

     

  • Provide opportunities to for students to revoice a mathematical thinking. Ask a few students to revoice the ideas used in this episode:

     

    • Revoice how you can determine the lengths of the sides of the right triangle.

    • Revoice how the lengths in the expressions can be seen on the graph.
    1. Why is the vertex labeled (h, k)? A general point on the graph is labeled (x, y). Why the difference?

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Mathematics in this Lesson

Lesson Description

 

Sasha and Keoni develop the vertex form of the equation of a parabola as y = (x–h)2/(4p) + k where the (h,k) is the vertex and p the distance from the vertex to the focus.