Question

A ball is thrown in the air from a platform. The path of the ball can be modeled by the function h(t)=-16 t^{2}+32t+4 where h(t) is the height in feet and t is the time in seconds.How long does the ball take to reach its maximum height?

Answer 1

1 second

Step-by-step explanation:

The equation that models the path of the ball is given below:

`h\mleft(t\mright)=-16t^2+32t+4`

To determine how long it takes the ball takes to reach its maximum height, we find the equation of the line of symmetry.

`\begin{gathered} t=-(b)/(2a),a=-16,b=32 \\ t=-(32)/(2(-16)) \\ =-(32)/(-32) \\ t=1 \end{gathered}`

Thus, we see that it takes the ball 1 second to reach its maximum height.