A ball is thrown into the air with an upward velocity of 32 ft/s. its height h in feet after t seconds is given by the function h = -16t^2+ 32t+ 6. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary what is the balls maximum height?
To find the time at which the ball reaches its maximum height, we need to determine the vertex of the parabolic function h = -16t^2 + 32t + 6.
The vertex of a parabola is given by the formula t = -b/(2a), where a and b are the coefficients in the quadratic equation. In this case, a = -16 and b = 32.
t = -32/(2 * -16) = -32/-32 = 1
Therefore, the ball reaches its maximum height after 1 second.
To find the maximum height, substitute t = 1 into the equation h = -16t^2 + 32t + 6.
h = -16(1)^2 + 32(1) + 6 = -16 + 32 + 6 = 22
Therefore, the ball reaches a maximum height of 22 feet.