A person standing close to the edge on top of a 144-foot building throws a ball vertically upward. The quadratic function $\displaystyle {h}{\left({t}\right)}=-{16}{t}^{{2}}+{128}{t}+{144}$ models the ball's height about the ground, $\displaystyle {h}{\left({t}\right)}$, in feet, $\displaystyle {t}$ seconds after it was thrown.

a) What is the maximum height of the ball?

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b) How many seconds does it take until the ball hits the ground?

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