Graph the system of linear inequalities.
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The line of symmetry for the parabola described by
... y = ax²+bx+c
is given by
... x = -b/(2a)
That line for your parabola is
... t = -24/(2×(-16)) = 24/32 = 3/4 = 0.75
The vertex (maximum) lies on this line. The value of h at that point is
... h = -16(3/4)² + 24(3/4) + 7 = -9 + 18 + 7 = 16
The ball reaches its maximum height in 0.75 seconds.
The ball's maximum height is 16 ft.
