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 do we call the point where a maximum occurs? Find the axis of symmetry formula and write it.
To find the time at which the diver reaches maximum height, we can first find the axis of symmetry. The axis of symmetry formula for a parabolic function in the form of f(t) = at^2 + bt + c is t = -b/(2a). In this case, a = -16 and b = 16, so:
t = -16/(2 * -16) = 16/32 = 0.5 seconds
At this time, the diver will reach the maximum height. To find this height, plug this time value into the function:
h = -16(0.5)^2 + 16(0.5) + 12 = -16(0.25) + 8 + 12 = -4 + 8 + 12 = 16 feet
The maximum height the diver reaches is 16 feet.
We call the point where a maximum occurs the vertex of the parabola.
The axis of symmetry formula for this function is t = -b/(2a), which simplifies to t = -16/(2 * -16) = 1/2.