Parabolas Lesson 2 Episode 3 (Teachers)


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Sasha and Keoni justify how their three methods for finding points on a parabola satisfy the criteria in the definition of a parabola.

Episode Supports

Students’ Conceptual Challenges

Representing an unknown distance on the grid can be challenging. Here the distance from the point on the parabola when y = 5 and the y-axis is unknown [1:32].

Sasha and Keoni incorrectly label this distance as b2 [1:37] but correctly treat it as b, which is  4.5 [2:42]. This inconsistency is addressed later in Lesson 3, Episode 4.

Focus Questions

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

1. [Pause video at 1:40]. How does Keoni know that the distance from the point on the parabola to the focus is 6?

2. [Pause video at 2:50]. Sasha wrote 4.5 above the b2.  What does the 4.5 represent?

Supporting Dialogue

Ask your students to reflect on the usefulness of the Pythagorean theorem by asking:

1. Why does the Pythagorean theorem work here?

2. How do the lengths of the sides of the triangle help you find the coordinates of the point on the parabola?

Math Extensions

1. A circle is the set of points that are equal distance from a fixed point (called the center).  The graph below is of a circle with the center at the origin. Can you find the x-value of a point on the circle below when the y-value is 4? Explain your reasoning.

2. Find the x-value of a point on the circle shown below when the y-value is 2. Explain your reasoning.

Parabolas L2 E3 Math extension image