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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?

A ball is thrown in the air from a platform The path of the ball can be modeled by the function ht16 t232t4 where ht is the height in feet and t is the time in class=

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Answer:

1 second

Explanation:

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

[tex]h\mleft(t\mright)=-16t^2+32t+4[/tex]

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

[tex]\begin{gathered} t=-\frac{b}{2a},a=-16,b=32 \\ t=-\frac{32}{2(-16)} \\ =-\frac{32}{-32} \\ t=1 \end{gathered}[/tex]

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

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