The Parabolic Pathfinder

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A parabolic path is modeled by the quadratic equation

�=−2�2+12�−10, where � represents the height in meters above ground and � represents the horizontal distance in meters from the starting point.

  1. At what horizontal distances � is the path exactly 6 meters above the ground?
  2. What is the maximum height reached by the path and at what horizontal distance does this occur?

Provide your answers in terms of meters and round to two decimal places if necessary.

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