Exploring a Parameter Change
Keoni and Sasha compare the graphs of y = x2/(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 = x2/(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 = x2/(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=x2 and y=x2/2). 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: Reflecting
Sasha and Keoni reflect on their graphs of y = x2/(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.