Getting and Using Geometric Information
Given the equation of a parabola in any form, Sasha and Keoni find geometric information (such as the focus, directrix, p-value, and vertex) about the parabola.
Episode 1: Making Sense
Keoni and Sasha begin to find geometric information from the equation, y = (x–2.4)2/6, in vertex form. They find the p-value and determine the vertex of the parabola.
Episode 2: Exploring
Sasha and Keoni graph the equation y = (x–2.4)2/6. They determine the coordinates of the focus and the equation of the directrix from the geometric information in the equation.
Episode 3: Repeating Your Reasoning
Keoni and Sasha look for geometric information of a parabola represented by the equation y = 2(x – 3)2 + 1. They start by finding the vertex and the p-value.
Episode 4: Making Sense
Keoni and Sasha examine an equation of a parabola in a different form, y = x2 – 4x + 4. When they look for geometric information, the p-value and vertex are not apparent. They start by rewriting the equation.
Episode 5: Exploring
Sasha and Keoni examine yet another equation of a parabola that is not in vertex form, y = x2 – 4x + 5. They start out by seeking a method to re-express the equation in vertex form.