A volleyball is his upward by a player in a game. The height h (in fee) of the volleyball after t seconds is given by the function h=-16t^2+30t+6.
What is the maximum height of the volleyball? explain your reasoning.
To find the maximum height of the volleyball, we need to determine the vertex of the quadratic function h(t) = -16t^2 + 30t + 6. The vertex represents the highest point of the parabolic curve, which is the maximum height in this case.
To find the vertex, we can use the formula: t = -b / (2a), where a, b, and c are the coefficients of the quadratic function. In our case, a = -16 and b = 30.
Substituting the values into the formula, we find:
t = -(30) / (2(-16))
t = -30 / -32
t = 15/16
Now that we have the value of t, we can substitute it into the original function to find the maximum height (h):
h = -16(15/16)^2 + 30(15/16) + 6
Calculating this expression gives us:
h = -16(225/256) + 450/16 + 6
h = -225/16 + 450/16 + 6
h = 225/16 + 450/16 + 96/16
h = 771/16
Therefore, the maximum height of the volleyball is 771/16 feet.