 # Standard #: MAFS.912.G-GPE.1.2 (Archived Standard)

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Derive the equation of a parabola given a focus and directrix.

### General Information

Subject Area: Mathematics
Domain-Subdomain: Geometry: Expressing Geometric Properties with Equations
Cluster: Translate between the geometric description and the equation for a conic section. (Geometry - Additional Cluster) (Algebra 2 - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved - Archived

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#### Lesson Plans

 Name Description I'm Focused on the Right Directrix In this lesson, the geometric definition of a parabola is introduced. Then students learn how to write the equation of a parabola in vertex form given its focus and directrix. Discovering Properties of Parabolas by Comparing and Contrasting Parabolic Equations Teachers can use this resource to teach students how to derive the equation of a parabola in vertex form y = a(x – h)2 + k, when given the (x, y) coordinates of the focus and the linear equation of the directrix. An additional interactive graphing spreadsheet can be used as a resource to aid teachers in providing examples. Acting Out A Parabola: the importance of a vertex and directrix Students will learn the significance of a parabola's vertex and directrix. They will learn the meaning of what exactly a parabola is by physically representing a parabola, vertex, and directrix. Students will be able to write an equation of a parabola given only a vertex and directrix. Explore the Properties of a Parabola and Practice Writing its Equation This lesson provides an opportunity for students to: confirm the definition of a parabola by measuring the distances from parabola points to its focus and the directrix; discover parabolic parameters by measuring the distances from its focus to its vertex ("p"), its vertex to the directrix ("p"), and the length of its latus rectum ("4p"); test the vertex-directrix form of parabola equation by choosing random values of the directrix' length and the coordinates of the vertex, using those values in writing vertex-directrix form of parabolic equations, and then by using graphing calculators identifying the type of curves described by those equations. As a result of this lesson, students will learn the properties of parabola, be able to write an equation of a parabola given a focus and directrix, and will demonstrate these skills in completing the Independent Practice worksheet. Definition of a Parabola Student will learn how to determine an algebraic representation of a parabola, given its focus and its directrix. Anatomy of a Parabola Graphic and analytic means are used to write the equation of a parabola given its focus and directrix. The Math Behind the Records Students will develop an understanding of how the position of the focus and directrix affect the shape of a parabola. They will also learn how to write the equation of a parabola given the focus and directrix. Ultimately this will lead to students being able to write an equation to model the parabolic path an athlete's center of mass follows during the high jump. A Point and a Line to a Parabola! In this lesson, the student will use the definition of a parabola and a graphing grid (rectangular with circular grid imposed) to determine the graph of the parabola when given the directrix and focus. From this investigation, and using the standard form of the parabola, students will determine the equation of the parabola. Introduction to the Conic Section Parabola This lesson is an introduction into conic sections using Styrofoam cups and then taking a closer look at the parabola by using patty paper to show students how a parabola is formed by a focus and a directrix.

#### Perspectives Video: Teaching Idea

 Name Description Representations of Parabolic Functions Don't get bent out of shape! Here's some ideas about how parabolic functions are connected to the real world and different ways they can be represented.

#### Worksheet

 Name Description Reflection by a Parabola Students will use the construction of copying an angle to implement the reflection of rays off a parabola. The students will observe that the reflected rays all pass through a common point, the focus.
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