The height of a tennis ball is modeled by the equation h(t)=-9.8tsquared+4t+1 where h is the height of the ball in meters and t is the time in seconds, find the maximum height of the ball.

The
height of the tennis ball h(t) = –9.8t^{2}
+ 4t + 1 is a quadratic function of time. Since its leading
coefficient

a = –9.8 is negative, the function has a maximum at t_{0}
= – 4/(2(–9.8)) = 0.203 s and equals h(t_{0})
= –9.8 t_{0}^{2}
+ 4 t_{0}+
1 = –9.8 ·0.203^{2}
+ 4·0.203+
1 = 1.4 m.