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.<\/p>\n\n\n\n
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.<\/p>\n\n\n\n
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).<\/p>\n\n\n\n
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).<\/p>\n\n\n\n
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 (\u20133, 0).<\/p>\n\n\n\n
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).<\/p>\n\n\n\n
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).<\/p>\n\n\n\n
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.<\/p>\n\n\n\n