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 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 can be defined by finding the values of t that make the equation h=-16t^2+33t+6 equal to the maximum height.
To find the maximum height, we can find the vertex of the quadratic equation h=-16t^2+33t+6. The vertex can be found using the formula t=-b/2a, where 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 >= 33/32.