Sasha and Keoni use points on three parabolas that share a y-value to explain why increasing the p-value results in the parabola getting wider on the coordinate grid.
Students’ Conceptual Challenges
Sasha and Keoni are examining the equation 16 = x2/p when they are asked that happens to x when p increases. They pause as they search for an explanation [4:21].
➤ By using algebra to rewrite the equation so that the variables are expressed in a direct relation with each other, x = 4√p, Sasha and Keoni find a way to respond to the question. The direct representation supports their reasoning on how a change in the p-value impacts the x-value.
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 1:53]. Keoni considers a parabola that goes through the origin and contains the point (4.5. 4). Can someone come up here and draw the rest of the parabola and estimate where the focus would be?
2. [Pause video at 6:44]. How did Keoni and Sasha get the equation x = 4√p?
Support the opportunity for students to engage in precise language as they articulate mathematical claims:
1. As the x-value changes, how does the focus change?
2. Restate the claim and reasoning Sasha and Keoni use to argue why the parabola gets wider as the p-value increases.
1. Find the coordinates of points on each of the three parabolas when the y-value is 1.
2. Considering the ordered pairs that you found, what do you notice about the x-values when the p-value increases? How does that impact the width of the parabola as the p-value changes?