(adsbygoogle = window.adsbygoogle || []).push({}); 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).

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

Can you offer guidance or do you also need help?

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