# Parabolas Lesson 9 Episode 7 (Teachers)

### Exploring

In the last episode Sasha and Keoni determined the distances of the sides of a right triangle on a general parabola with vertex (h, k) and distance p from the vertex to the focus. Next they derive the equation for the parabola by substituting those distances into the Pythagorean Theorem.

### Episode Supports Focus Questions

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?

Supporting Dialogue

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

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

2. Revoice how the lengths in the expressions can be seen on the graph.

Math Extensions

1. Why is the vertex labeled (h, k)? A general point on the graph is labeled (x, y). Why the difference?