Developing an Equation for a Parabola for Any Given y-Value
Keoni and Sasha create a general method for representing the x-value for any point on a particular parabola, given the y-value of that point. By using their previous results, along with the Pythagorean theorem, they are able to determine the equation for the parabola.
Sasha and Keoni grapple with how to represent a general point on the parabola and how to express different distances involving that point.
Keoni and Sasha develop an equation that relates the x-value to the y-value for a general point on a particular parabola.
Keoni and Sasha reflect on the meaning of their equation.
Keoni and Sasha determine the x-value of a point on the parabola with a y-value of 3.5.
Sasha and Keoni share ideas about the usefulness of the equation
x = √(4y), which they derived in Episode 2.