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Understanding Parabolas: A Concise Guide

Explore the essence of parabolas, their algebraic definition, reflective properties, and how the focus and directrix influence the shape and equation. Dive into examples with different vertex and focus positions.

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Understanding Parabolas: A Concise Guide

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Presentation Transcript

  1. What do we know about parabolas?

  2. Conic Slice

  3. Algebraic Definition Parabola: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is all of the points such that the distance to the focus equals the distance to the directrix. Focus: A given point inside the Parabola Directrix: A line perpendicular to the axis of symmetry

  4. Why do we have a focus point? -Reflective property

  5. Vertex: (0,0)

  6. What happens if the vertex is at the origin and the focus is to the right of the origin? -How would that change the equation

  7. Example #1 Vertex=(0,0) Focus=(0,-2)

  8. Example #2Vertex=(0,0) Directrix: y=-2

  9. Example #3Vertex=(0,0) Focus=(3,0)

  10. Example #4Vertex=(0,0) Directrix: x=3

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