Question

spencer hits a tennis ball past his opponent. the height of the tennis ball in feet is modeled by the equation h(t)=-0.075t^2+0.6x+2.5 where t is the time since the tennis ball was hit meausured in seconds. how long does it take for the ball to reach its maximum height?

Answer 1

The quadratic function is given by the equation
`h(t)=-0.075t^2+0.6t+2.5.`

The maximal height will be at vertex. Find t-coordinate of the parabola vertex:

`t_(vertex)=-(b)/(2a)=-(0.6)/(2\cdot (-0.075))=4\text{ seconds.}`

At t=4,

`h(4)=-0.075\cdot 4^2+0.6\cdot 4+2.5=-1.2+2.4+2.5=3.7\text { feet. }`

Answer: it will take 4 seconds for the ball to reach the maximal height of 3.7 feet.