Given function: h(t) = -16t^2 + 96t + 5, where t represents the time in minutes.
We need to find the interval for which the arrow is going up.
The arrow is going up would be the values of time t =0 when it start and when it went to highest point.
Given function is a quadratic function and it represents a parabolic shape.
The highest point on the parabola is a vertex point.
Therefore, we need to find the x-coordinate of the vertex.
We know, formula for x-coordinate of the vertex is
[tex]\frac{-b}{2a}[/tex]
For the given quadratic a= -16 and b=96.
Plugging values of a and b in formula, we get
[tex]\frac{-96}{2(-16)}=\frac{-96}{-32} = 3.[/tex]
Therefore, after 3 seconds arrow would be at maximum height.
Therefore, the interval for which the arrow is going up is [0,3].
