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Parabolas

Parabolas. History Equation Graph Applications. History. Studied by Menaechmus, pupil of Plato Was written about by Euclid Named by Apollonius Focus and directrix considered by Pappus Galileo showed projectiles follow parabolic paths. Equation.

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Parabolas

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  1. Parabolas • History • Equation • Graph • Applications

  2. History • Studied by Menaechmus, pupil of Plato • Was written about by Euclid • Named by Apollonius • Focus and directrix considered by Pappus • Galileo showed projectiles follow parabolic paths

  3. Equation • The set of points in a plane that are equidistant from a point (focus) and a line (directrix). • Standard Form • y = Ax2 + Bx +C • y = a(x - h)2 + k

  4. Graph • What are some examples of a parabola? Where do we find them in the world? • Try graphing a parabola. • Click on picture of the parabola. • Go to file New Sketch. • Make a random point. • Make a random line. • Select both the line and the point. • Press Play and watch the parabola form.

  5. Identify the parabolas in the pictures

  6. Applications • To map the path of projectiles, like a baseball, in a homerun, a golf shot, or a cannonball. • Show the path of light rays • Ideal shape for cables on a suspension bridge • Shape of a water spout

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