You throw a ball straight up from a rooftop 70 feet high with an initial speed of 48 feet per second. The function s(t)=−16t2+48t+70 models the​ ball's height above the​ ground, s(t),in​ feet, t seconds after it was thrown. During which time period will the​ ball's height exceed that of the​ rooftop?

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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.