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Quadratic Functions and Their Graphs

Identify the intercepts, vertex, and axis of symmetry

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Keep the Focus

Credit: John W. Ciccarelli Jr./U.S. Navy
Source: https://en.wikipedia.org/wiki/File:The_Mobile_User_Objective_System.jpg
License: CC BY-NC 3.0

Ever wonder how cell phones, television, and the Internet work no matter your location? With the help of parabolas, satellites send signals to your device, whether it is a smartphone, tablet, or TV.

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Satellites act as very large mirrors. They reflect signals from the Earth to other satellites before finally reaching your device. It is important for engineers to create satellites with the optimal shape to allow for effective signal reflection?this is where parabolas come in. The special curve of a parabola allows for the maximum amount of reflection from incoming signals. Satellites are designed like three-dimensional parabolas.

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

Because of its parabolic shape, a satellite is able to reflect signals received anywhere on the dish inward to the same point each time. This special point is called the focus of the parabola. By placing an antenna at the focus of the satellite, engineers can be sure that all incoming signals to the dish will be transmitted to their destination, giving you a clear cable picture or a signal on your smartphone.

See for yourself: 
http://jwilson.coe.uga.edu/EMAT6680Fa08/Wisdom/EMAT6690/Parabolanjw/reflectiveproperty.htm

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Have you heard of Archimedes' "death ray"? Find out how the ancient Greeks used the same property of parabolas that we use for satellites in warfare.

http://www.mathsinthecity.com/examples/satellite.html

Test your parabolic expertise with these questions:

  1. What 3D shape when sliced produces a parabola?
  2. What happens to a light placed at the focus of a parabolic mirror?
  3. What was the death ray's tactic?

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Image Attributions

  1. [1]^ Credit: John W. Ciccarelli Jr./U.S. Navy; Source: https://en.wikipedia.org/wiki/File:The_Mobile_User_Objective_System.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0

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