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Lesson 6:

Exploring a Parameter Change

Keoni and Sasha compare the graphs of y = x^{2}/(4p) for p-values of 1/4, 1/2, and 1. They figure out the effect that changing the value of p has on the graph of the parabola.

Episode 1: Making Sense

Sasha and Keoni use the equation y = x^{2}/(4p) to plot a parabola for p = 1/4. They make a conjecture for how the shape of the parabola will change as gets larger.

Episode 2: Exploring

Keoni and Sasha continue to explore the role that the p-value has on the shape of the graph of parabolas represented by y = x^{2}/(4p). They graph a parabola with a p-value of 1/2, and compare it to the graph of a parabola with a p-value of 1/4 from Episode 1.

Episode 3: Reflecting

Keoni and Sasha reflect on the two parabolas that they graphed in Episodes 1 and 2 (y=x^{2} and y=x^{2}/2). They notice several features of the parabolas that change when the p-value increases from 1/4 to 1/2.

Episode 4: Repeating Your Reasoning

Keoni and Sasha continue to increase the p-value and investigate what happens to the graph of the parabola. In this episode, they graph a parabola with a p-value of 1.

Episode 5: Making Sense

Sasha and Keoni reflect on their graphs of y = x^{2}/(4p) with p-values of 1/4, 1/2, and 1. They consider the effect of increasing and decreasing the p-value on the graph of the parabola.