A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)= 96t-16t^2 . After how long will it reach its maximum height? Do not round your answer.Time: ___ seconds

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The axis of symmetry is the x coordinate of the vertex and the absolute maximum/minimum value of f(x) is at the y-coordinate of the vertex of a parabola or quadratic function of the form ax^2+bx+c The vertex will always have the coordinates: x=-b/(2a) and y=(4ac-b^2)/(4a) Since we only need to know the time when it reaches its maximum height we can simply solve for the x coordinate which is time in this circumstance. so: t=-b/(2a)=-96/(-16*2)=3 seconds

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