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=−16t^2+33t+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
The domain of the ball when it reaches its maximum height is given by the time values for which the height is defined and exists.
In this case, the height equation is h = -16t^2 + 33t + 6. Since the height represents the height of the ball, it cannot be negative or undefined.
To find the domain when the ball reaches its maximum height, we need to find the time at which the height is at its maximum. The maximum height occurs at the vertex of the parabolic equation.
The vertex of a parabola in the form h = at^2 + bt + c is given by t = -b / (2a).
In this case, a = -16 and b = 33.
t = -33 / (2 * -16) = -33 / -32 = 33/32.
Since time cannot be negative, the domain of the ball when it reaches its maximum height is t ≥ 0.