Explaining 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 Sasha and Keoni use algebraic and geometric thinking to form three arguments that justify why a parabola gets wider on the coordinate grid as the p-value in y = x2/(4p) increases.
Episode 1: Making Sense
Sasha and Keoni review the relationship that they discovered between the value of p in the equation y = x2/(4p) and the width of the graph of the parabola.
Episode 2: Exploring
Keoni and Sasha use points that share an x-value to explain why increasing the p-value in the equation y = x2/(4p) results in the parabola getting wider.
Episode 3: Reflecting
Keoni and Sasha reflect on why increasing the p-value results in a wider parabola. They engage in algebraic reasoning to support their argument.
Episode 4: Repeating Your Reasoning
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.
Episode 5: Making Sense
Sasha and Keoni use “the special points” on the three parabolas to generate another explanation for why increasing the p-value results in the parabola getting wider on the coordinate grid.
Episode 6: Exploring
Sasha and Keoni use what they know about special points to explain why increasing the p-value results in the parabola getting wider on the coordinate grid.