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Parabola

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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

2

,

.

y ax bx c

or

f x ax bx c

= + +

= + +

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Conic Sections and Shapes

Hyperbola

Parabola

Circle

Ellipse

Parallel to the side

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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

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Trajectory for Launched Object

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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 1.8-G

Source: NASA-MSFC

Plane at 45 ° Plane at 45 °

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Parabolic Concentration

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Concentration Examples

Satellite antenna

Source: NASA-GRC

Technology satellite

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Concentration Examples Trough solar dish

Source: Sandia National Laboratories

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Parabolic Dispersion

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Dispersion Examples

Source: www.Pics4Learning.com

Parabolic reflector

Reflected light forms a parallel beam directed straight ahead.

Focus

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Parabolic Curves in Sports

Source: www.Pics4Learning.com

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Parabolic Curves at Home

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Architecture San Francisco Golden Gate Bridge

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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?

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Application of a Parabola Used with permission by:

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