IM Geo.6.8 Lesson: Equations and Graphs
The image shows a parabola with focus and directrix (the -axis). Points , , and are on the parabola.
Without using the Pythagorean Theorem, find the distance from each plotted point to the parabola’s focus. Explain your reasoning.
The image shows a parabola with focus and directrix (the -axis).
Write an equation that would allow you to test whether a particular point is on the parabola.
The equation you wrote defines the parabola, but it’s not in a very easy-to-read form. Rewrite the equation to be in vertex form: , where is the vertex.
Match each graph with the equation that represents it.
In this section, you have examined points that are equidistant from a given point and a given line. Now consider a set of points that are half as far from a point as they are from a line. Write an equation that describes the set of all points that are as far from the point as they are from the -axis.
Use technology to graph your equation. Sketch the graph.
Describe what it looks like.