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Lesson 10:

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 = x^{2} – 4x + 4. When they look for geometric information, the p-value and vertex are not apparent. They start by rewriting the equation.

Episode 5: Reflecting

Sasha and Keoni examine yet another equation of a parabola that is not in vertex form, y = x^{2} – 4x + 5. They start out by seeking a method to re-express the equation in vertex form.