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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.
y = ax 2 + bx + c ,
or
f ( x ) = ax 2 + bx + c.
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Conic Sections and Shapes
Parallel
to the
side
Parabola
Hyperbola
Circle
Ellipse
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Parabolic Curve Applications
Everyday
• Nature’s parabolas
• Architecture
• Home
• Tools
In
physics
• Parabolic trajectory
• Zero gravity
In technology
• Parabolic antennas
and satellites
• Solar
• Parabolic reflection
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Trajectory for Launched Object
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Trajectory: NASA Zero G Aircraft
Parabolic Flight
30 thousand feet
28
26
Plane at 45 °
Plane at 45 °
Zero-G
24
22
1.8-G
1.8-G
20
0
20
Duration (seconds)
6
Source: NASA-MSFC
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Parabolic Concentration
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Concentration Examples
Satellite antenna
Technology satellite
Source: NASA-GRC
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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
Parabolic
reflector
Reflected
light forms
a parallel
beam
directed
straight
ahead.
Source: www.Pics4Learning.com
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
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2013 IEBC
SLATE Demonstration Curricula
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