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.
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?
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