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Derive the equation of a parabola given a focus and directrix.
Standard #: MAFS.912.G-GPE.1.2Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Expressing Geometric Properties with Equations
Cluster: Level 2: Basic Application of Skills & Concepts
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 Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Related Courses
Related Resources
Lesson Plans
  • I'm Focused on the Right Directrix # In this lesson, the geometric definition of a parabola is introduced. Students will also 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 # Students learn parabola properties, how to write parabola equations, and how to apply parabolas to solve problems.
  • Definition of a Parabola # Student will learn the algebraic representation of a parabola, given its focus and its directrix.
  • Anatomy of a Parabola # Students learn the parts of a parabola and write its equation given the focus and directrix. A graphic organizer is used for students to label all parts of the parabola and how it is created.
  • 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
  • Representations of Parabolic Functions # <p>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.</p>
Worksheet
  • 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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