Sasha and Keoni discuss what the equation y = x2/(4p) means. They also use it to find the equation of a parabola with a vertex at the origin and a focus at (0, 0.5).
Episode Supports
Students’ Conceptual Challenges
Students may have difficulty understanding the role that the parameter, p, plays in the equation y = x2/(4p). It may be confusing that the equation represents a family of parabolas.
➤ By using the equation y = x2/(4p) to graph a particular parabola (when p = 0.5), Keoni and Sasha gain insight into how the equation y = x2/(4p) can generate different parabolas, all with a vertex at the origin, by changing the p-value.
Focus Questions
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 0:59]. List everything you know about the parabola with a vertex at the origin and a focus 1/2 unit above the origin.
2. [Pause video at 6:35]. List everything you know about the equation y=x2/(4p).
Supporting Dialogue
Invite students to engage in a pair-share activity as they respond to each focus question:
1. With your partner, make a list of what you know about the parabola with a vertex at the origin and a focus 1/2 unit above the origin. Prepare your answers to share with the whole class.
2. With your partner, make a list of what you know about the equation y = x2/(4p). Prepare your answers to share with the whole class.
Math Extensions
Consider the graph below.
1. Consider the two parabolas graphed below. Use the equations for each graph and geometric reasoning to label the coordinates of 4 points on each graph.
2. Compare the points and coordinates across the two parabolas. List any patterns that you notice.
Graph of parabolas is missing—in the original document.
