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).