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

Question

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

1.03 seconds
1.03 seconds

23.01 feet
23.01 feet

1.22 seconds
1.22 seconds

−1.03 seconds
negative 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 \( t \) at which the maximum height occurs is given by:

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

In this case, the equation is:

\[ h(t) = -16t^2 + 33t + 6 \]

Here, \( a = -16 \) and \( b = 33 \). Plugging in these values:

\[ t = -\frac{33}{2 \cdot -16} = \frac{33}{32} \approx 1.03125 \]

This rounds to approximately 1.03 seconds.

So the domain of the ball when it reaches its maximum height is 1.03 seconds.