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