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.
Episode Supports
Students’ Conceptual Challenges
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].
Focus Questions
For use in a classroom, pause the video and ask these questions:
1. [Pause the video at 0:50]. Sasha and Keoni just wrote down a long algebraic equation. Where did it come from?
2. [Pause the video at 1:45]. Sasha said that they know where they are going. What do we think? What equation do you predict will emerge as they solve for y?
Supporting Dialogue
Provide opportunities to for students to revoice mathematical ideas. Ask a few students to revoice the strategies used in this episode:
Revoice Sasha and Keoni’s strategies to solve for y.
Math Extensions
A student working on solving for y simplified an expression as shown below:
2(y–k)(p) + 2(y–k)(p) _________ 4(y–k)(2p)
Does this work? Does it not work? How do you know?
