The figure shows two lines: One line is the secant line between the origin and a point P on the parabola y = x2 The second line is the perpendicular bisector to the line segment OP. The perpendicular bisector, RQ, will always intersect OP at the midpoint between O and P, hence the name bisector. The point Q is where RQ intersects the y-axis. As Papproaches the origin, along the parabola, the point Q will "slide" along the y-axis. What is the limiting position for the point Q? y = x? R

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.