Answer: After [tex]3.5\ seconds[/tex]
Step-by-step explanation:
Knowing that after "t" seconds, its height "h" in feet is given by the function:
[tex]h(t) = 112t -16t^2[/tex]
The maximum height is the y-coordinate of the vertex of the parabola. Then, we can use the following formula to find the corresponding value of "t" (which is the x-coordinate of the vertex):
[tex]t=\frac{-b}{2a}[/tex]
In this case:
[tex]a=-16\\b=112[/tex]
Substituting values, we get that the ball will reach the maximum height after:
[tex]t=\frac{-112}{2(-16)}\\\\t=3.5\ seconds[/tex]
