Question

A volleyball is served by a 6-foot player at an initial upward velocity of 33 feet per second. The situation is modeled by the equation h=−16t2+33t+6
h
=
−
16
t
2
+
33
t
+
6
h representing the height in feet and t representing the time in seconds. Using this equation, define the domain of the ball when it reaches its maximum height.(1 point)
Responses

23.01 feet
23.01 feet

−1.03 seconds
−
1.03

seconds
negative 1.03 seconds

1.22 seconds
1.22 seconds

1.03 seconds

Answer 1

To find the time when the volleyball reaches its maximum height, we can use the vertex formula for a quadratic equation of the form \(h(t) = at^2 + bt + c\). The time at which the maximum height occurs is given by the formula:

\[
t = -\frac{b}{2a}
\]

In your equation:
- \(a = -16\)
- \(b = 33\)

Plugging in these values:

\[
t = -\frac{33}{2 \times -16} = \frac{33}{32} \approx 1.03125 \text{ seconds}
\]

Therefore, the volleyball reaches its maximum height at approximately \(1.03\) seconds.

The function \(h(t)\) describes the height of the volleyball as a function of time. The appropriate domain for the height of the volleyball to reach its maximum height would start from time \(t = 0\) (the time of the serve) and extend until \(t = 1.03\) seconds (the time it reaches maximum height). Typically, domain in this context is the interval of time during which the volleyball is in the air from the moment it is served until it reaches its peak.

In this case, since we are only looking for when it reaches the maximum height, the time is:

**1.03 seconds.**