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2013 IEBC www.iebcnow.org For more information on SLATE Demonstration Curricula, contact: Shelly Valdez, Ed.D IEBC Director of Educational Collaboration svaldez@iebcnow.org

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Parabola 1 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Parabola A parabola is a plane conic section curve formed by the intersection of a right circular cone and a plane parallel to a side of the cone. Mathematically, a parabola is the two-dimensional graph of a second-degree or quadratic equation or function of the form. 2 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Conic Sections and Shapes Hyperbola Parabola Circle Ellipse Parallel to the side 3 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Parabolic Curve Applications In technology Parabolic antennas and satellites Solar Parabolic reflection In physics Parabolic trajectory Zero gravity Everyday Nature’s parabolas Architecture Home Tools 4 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Trajectory for Launched Object 5 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Trajectory: NASA Zero G Aircraft Parabolic Flight 30 thousand feet 28 26 Zero-G 24 22 20 0 20 40 Duration (seconds) 1.8-G Source: NASA-MSFCNASA-MSFC Plane at 45 ° 6 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Parabolic Concentration 7 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Concentration Examples Satellite antenna Source: NASA-GRCNASA-GRC Technology satellite 8 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Concentration Examples Trough solar dish Source: Sandia National Laboratories 9 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Parabolic Dispersion 10 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Dispersion Examples Source: www.Pics4Learning.com Parabolic reflector Reflected light forms a parallel beam directed straight ahead. Focus 11 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Parabolic Curves in Sports Source: www.Pics4Learning.com 12 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Parabolic Curves at Home 13 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Architecture San Francisco Golden Gate Bridge 14 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Storming Castle Pi: Overarching Problem The Raving Irrationals are trying to overtake the Castle of Pi. They want to launch burning bales of hay into the castle to drive out the citizens of Pi. When the catapult arm is pulled back to ground level, the hay bale is launched at a distance of 100 feet west of the castle wall. The wall is 35 feet high. The bale clears the wall by a height of 15 feet and lands inside the castle, which is also 100 feet from the wall. The Irrationals come under attack and must retreat from this site. Their new position is 70 feet southwest of the wall. They need to relaunch; however, the wall on this side is 45 feet high. If the castle is 120 feet in diameter, will the hay bales land inside the castle wall or fly over it? 15 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Application of a Parabola Used with permission by: 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org

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Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley CHAPTER 7: Conic Sections 7.1 The Parabola 7.2 The Circle and the Ellipse 7.3 The.

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley CHAPTER 7: Conic Sections 7.1 The Parabola 7.2 The Circle and the Ellipse 7.3 The.

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