# Parabolas Lesson 3 Episode 2 (Teachers)

### Exploring

Keoni and Sasha develop an equation that relates the x-value to the y-value for a general point on a particular parabola.

### Episode Supports Students’ Conceptual Challenges

Students might wonder how to interpret more than one symbol in a general equation. Students are often asked to isolate a variable on one side of the equals sign with a number on the other side, e.g., they “solve for x” by finding a numerical value for x. Having it make sense that the symbols are representing a general point in the parabola is challenging.

Keoni protests “but there are two variables” when Sasha writes (y–1)2 + b2  = (y+1)2 [1:11-1:34]. By going back to work through a specific example 62 + b2 =  82, Sasha and Keoni identify the method to solve for b in the general case [1:47-4:50].

Focus Questions

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

1. [Pause video at 1:34]. What problem are Sasha and Keoni trying to solve?

2. [Pause video at 2:44]. Sasha and Keoni are working to solve for b. Work ahead from here. Then we will compare our work with theirs.

Supporting Dialogue

Invite students to engage in revoicing. Place a blank student worksheet under a document camera.

1. Can someone come up to the graph to draw and label the right triangle that Sasha and Keoni used in this problem?

2. Ask a student to revoice how a fellow student determined the side lengths.

Math Extensions

Use the Pythagorean theorem to represent the lengths of the right triangles described below.

1. A right triangle where one leg is half the length of the other leg.

2. A right triangle where the two legs are the same length.