- The heights of a ball (in feet) thrown with an initial velocity of 90 feet per second from an initial velocity of 90 feet per second from an initial height of 4 feet is given as a function of time t(in seconds)by s(t)= -16t^2+90t+4

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To find the maximum height of the ball, we need to determine the vertex of the parabolic function s(t) = -16t^2 + 90t + 4.

The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula:

t = -b / (2a)

In this case, a = -16 and b = 90. Substituting these values into the formula, we have:

t = -90 / (2(-16))

t = -90 / -32

t ≈ 2.8125

Therefore, the time at which the ball reaches its maximum height is approximately 2.8125 seconds.

To find the maximum height, substitute this time value back into the equation s(t):

s(2.8125) = -16(2.8125)^2 + 90(2.8125) + 4

s(2.8125) ≈ 228.75

Therefore, the maximum height of the ball is approximately 228.75 feet.