No captions Captions Stop the video above first if it is playing.
No captions Captions Stop the video above first if it is playing.
Sasha and Keoni use the Pythagorean theorem and the definition of a parabola to derive the equation for a parabola with a vertex at the origin and a distance of p between the focus and vertex.
Episode Supports
Focus Questions
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 2:25]. What are the lengths of the vertical lines that Sasha and Keoni just drew?
2. [Pause video at 6:09]. Finish writing the equation and then solve for y. [Then start the video again and stop at 7:58]. How did your solution method compare with Sasha and Keoni’s?
Supporting Dialogue
Provide opportunities for all your students to express their ideas verbally, by asking them to talk with a partner.
1. [Pause the video at 3:58]. Talk with your neighbor. Where does the term y – p come from and what does it mean?
2. [Pause the video at 7:58]. Talk with your neighbor. Where does the equation y = x2/(4p) come from? Where does the 4p come from?
Math Extensions
1. Examine the parabola with a vertex at the origin and a focus at (0, -2). A general point on the parabola is labeled (x, y). A right triangle was formed so that the hypotenuse connects the (x, y) and the focus. The lengths of the three sides of the right triangle are x, -y + 2, and -y – 2. Explain why:
the distance from (x, y) to the x-axis is -y.
the length of the vertical side of the right triangle is -y – 2.
the length of the hypotenuse of the right triangle is -y + 2.
the length of the horizontal side of the right triangle is x.
2a. Using the Pythagorean Theorem and the definition of a parabola, derive the equation of the parabola with a vertex at the origin and a focus at (0,-2).
2b. Compare your equation with the equation that Keoni and Sasha derived for a parabola with a vertex at the origin and a focus at (0,2). What do you notice?
Captions
