A diver diving into a pool can be modeled by the function h = -16t2 + 16t + 12 where h is the
height in feet above the water after t seconds.Determine how many seconds it will take the diver to reach the maximum height and find the
maximum height of the diver. Round to the nearest tenth, if necessary.
What is your plan for finding the maximum height of the diver?
To find the maximum height of the diver, we need to find the vertex of the parabolic function h = -16t^2 + 16t + 12. The vertex represents the highest point of the parabola.
To find the x-coordinate of the vertex, we use the formula: x = -b/2a, where a = -16 and b = 16.
x = -b/2a = -16/(2(-16)) = 0.5
So it will take the diver 0.5 seconds to reach the maximum height.
To find the maximum height, we substitute t = 0.5 into the function:
h = -16(0.5)^2 + 16(0.5) + 12 = 14
Therefore, the maximum height of the diver is 14 feet.