Exploring Parabolas with Vertex (h, k)
Sasha and Keoni use a GeoGebra applet to move parabolas to the left, right, up, and down. Then they develop equations for several different parabolas where the vertex is not at the origin.
Sasha and Keoni make sense of parameters that can change the vertex of a parabola on the coordinate grid. They also revisit what they already know about how the p-value changes the shape of the graph of the parabola.
Keoni and Sasha use the Pythagorean Theorem and the definition of a parabola to derive an equation of parabola with a p-value of 3 and a vertex at (7, 0).
Keoni and Sasha reflect on the similarities and differences between the equations for two parabolas that have the same p-values. One parabola has a vertex at (0, 0) while the other parabola has a vertex at (0, 7).
Sasha and Keoni extend their work from the last episode to derive the equation of another parabola. This time the vertex of the parabola is at (–3, 0).
Sasha and Keoni now consider how the equation of the parabola will change if the parabola moves up on the coordinate grid. They derive an equation for a parabola with a vertex at (0, 2).
Sasha and Keoni notice patterns in the equations they have derived for parabolas with the same p-values for different vertices. They predict an equation for a parabola with a p-value of 3 and a vertex at (7, 2).
Keoni and Sasha examine a table with the equations they have explored so far. They use the table to predict an equation for a parabola with any given vertex.