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Arkimedes for a equation y=x(2-x) and x-axis

  1. Dec 10, 2011 #1
    1. Examine what the relationship is by calculating the parabolic segment and the
    inscribed triangle bounded by the function
    y =-x2 + 2x and the x-axis.

    2. Description:
    A horizontal line intersects a second degree curve in the points A and B. The line AB and
    quadratic curve enclosing an area. This area is called a parabolic segment. it
    tangent to the curve which is parallel to the chord AB tangent to the curve in C.
    The Greek mathematician, physicist and inventor Archimedes (287-212 BC) discovered
    that the area of triangle ABC and the area of ​​the parabolic segment always has the same
    relationship.


    3. The attempt at a solution:
    I found two pints on x-axis that where the parabola is intersected but the problem comes with finding the third point of the triangle, where a tangent intersect the parabola parallel to the x-axis. The two points are (0,0) and (-2,0).
     
  2. jcsd
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