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.
height of the tennis ball h(t) = –9.8t2
+ 4t + 1 is a quadratic function of time. Since its leading
a = –9.8 is negative, the function has a maximum at t0
= – 4/(2(–9.8)) = 0.203 s and equals h(t0)
= –9.8 t02
+ 4 t0+
1 = –9.8 ·0.2032
1 = 1.4 m.
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