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Quadratic Functions and Their Graphs

Identify the intercepts, vertex, and axis of symmetry

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Parabolic Perfection

Credit: Chris J. Nelson
Source: http://commons.wikimedia.org/wiki/File:Leon_Powe_Free_Throw.jpg
License: CC BY-NC 3.0

Do you think a computer’s calculations could help you perfect your free-throw shot more successfully than a coach? Inventors of a new sports technology tool think so. The parabolic path of a basketball shot can be interpreted and measured with math!

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In the early 2000s, four Silicon Valley friends put their heads together and created Noah, a sports technology machine intended to help basketball shooters “build the perfect arc.” If you picture a free throw as an upside-down parabola, you might see how being able to mathematically measure that parabola could help you analyze your shot. Noah’s Arc does just this. The machine measures the angle of the shot’s arc as well as the shot's depth at entry of the hoop and gives verbal feedback to the practicing shooter.

Credit: j9sk9s
Source: http://www.flickr.com/photos/j9sk9s/4128778346/
License: CC BY-NC 3.0

You use math every time you adjust your free throw. Shooting with a higher arc is like increasing the coefficient, \begin{align*}a\end{align*}, to make a “skinnier” parabola, and shooting with a flatter arc is like decreasing that coefficient to make the parabola “flatter.” By making these kinds of adjustments, you’re performing mental dilations! While Noah's feedback doesn't include your arc coefficients, it helps you work towards what research has shown to be the optimal arc: an angle of 45 degrees and a depth of 11 inches past the front rim.

See for yourself: http://www.noahbasketball.com/optimal_arc.php

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Learn more about Noah’s Arc and parabolas in basketball with the links below.



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Image Attributions

  1. [1]^ Credit: Chris J. Nelson; Source: http://commons.wikimedia.org/wiki/File:Leon_Powe_Free_Throw.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: j9sk9s; Source: http://www.flickr.com/photos/j9sk9s/4128778346/; License: CC BY-NC 3.0

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