Connecting Geometry with Algebra
Keoni and Sasha work with a parabola on the coordinate grid. They use the properties of the grid and the Pythagorean theorem to determine if the coordinates of a point are on a given parabola. They apply these methods to find the missing x-value of a point on the parabola for a given y-value.
Episode 1: Making Sense
Keoni notices that the grid allows them to measure the distance between some points and lines. Sasha and Keoni use the grid and the definition of a parabola to validate that three points are on the parabola.
Episode 2: Exploring
Sasha and Keoni use the Pythagorean theorem to justify why (4,4) is a point on the parabola.
Episode 3: Exploring
Sasha and Keoni justify how their three methods for finding points on a parabola satisfy the criteria in the definition of a parabola.
Episode 4: Repeating Your Reasoning
Keoni and Sasha extend their use of the Pythagorean theorem. They determine the x-value for a point on the parabola that has a y-value of 5.
Episode 5: Repeating Your Reasoning
Sasha and Keoni find the x-value of a point on the parabola with a y-value of 10.