Question

a person who is 5 feet tall throws a ball into the air at 100 feet per second. the function $h(t) = -16t^2 + 100t + 5$ models the height of the ball from the ground at any given second, $t$, and is shown in the graph (a parabola with time (seconds) on the x - axis and height of the ball (feet) on the y - axis, with points like around t=0, height near 5; t=1, height around 89; t=3, height around 157; t=6, height near 0).

Explanation:

Since the problem is not fully stated (e.g., what is being asked about the function or the graph), we can't proceed with a solution. But if we assume a common question like finding the time to reach maximum height, here's how:

Step1: Recall vertex formula for parabola

For a quadratic function \( h(t) = at^2 + bt + c \), the time \( t \) at vertex (max height for \( a < 0 \)) is \( t = -\frac{b}{2a} \). Here, \( a = -16 \), \( b = 100 \).

Step2: Calculate \( t \)

Substitute \( a \) and \( b \) into formula: \( t = -\frac{100}{2(-16)} = \frac{100}{32} = 3.125 \) seconds.

(Note: If the actual question is different, adjust steps accordingly. Since the original question is incomplete, this is a sample approach.)

Answer:

(Depends on the actual question. For sample max time: \( \boldsymbol{3.125} \) seconds)