Episode 1: Making Sense

Sasha and Keoni examine the similarities and differences between two parabolas with vertices on the origin but with different distances to the fo-cus. They determine if the same equation could represent both parabolas.

Episode 2: Exploring

Keoni and Sasha develop an equation for a parabola with a focus at (0,2) and a directrix of y = –2. They use the Pythagorean theorem and the definition of a parabola.

Episode 3: Reflecting

Keoni and Sasha compare the equations for two parabolas:  y = x²/8 and y = x²/4. and They make two different conjectures about the equation for a parabola with a focus at 3 units above the vertex.

Episode 4: Repeating Your Reasoning

Keoni and Sasha determine the equation of a parabola with a vertex at (0,0) and distance of three units between its focus and vertex. They compare the equation to their conjectures from Episode 3.

Episode 5: Making Sense

Sasha and Keoni make a prediction about an equation for any parabola with a vertex on the origin.

Episode 6: Exploring

Sasha and Keoni use the Pythagorean theorem and the definition of a parabola to derive the equation for a parabola with a vertex at the origin and a distance of p between the focus and vertex.

Episode 7: Reflecting

Sasha and Keoni discuss what the equation y = x2/(4p) means. They also use it to find the equation of a parabola with a vertex at the origin and a focus at (0, 0.5).