A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 52t - 16t^2 . What is the maximum height that the ball will reach?Do not round your answe

Answer:42.25 feetStep-by-step explanation:The height function is a parabola.  The maximum value of a negative parabola is at the vertex, which can be found with:x = -b/2awhere a and b are the coefficients in y = ax² + bx + c.Here, we have y = -16t² + 52t.  So a = -16 and b = 52.  The vertex is at:t = -52 / (2×-16)t = 13/8Evaluating the function:h(13/8) = -16(13/8)² + 52(13/8)h(13/8) = -169/4 + 169/2h(13/8) = 169/4h(13/8) = 42.25