Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-If a projectile is launched upward from a height of 32 feet at an initial velocity of 64 feet per second, then its height after t seconds is given by the function $h ( t ) = - 16 t ^ { 2 } + 64 t + 32$
A) 1 seconds
B) 2 seconds
C) 4 seconds
D) 8 seconds

Question

Quizplus · Accepted Answer

Fixed points occur when the output of the function equals the input, which is not applicable in this context since the function describes height over time, not a transformation from inputs to equivalent outputs. However, solving $h(t) = -16t^2 + 64t + 32 = t$ doesn't make sense in this physical context. The misunderstanding seems to be about finding the time when the height is maximum or solving for a specific height, which is not the same as finding a fixed point in the mathematical sense. The correct approach to find the time of maximum height is to use the vertex formula for a parabola, $t = -b/(2a)$, where $a = -16$ and $b = 64$, leading to $t = -64 / (2 * -16) = 2$.

Find All Fixed Points for the Function by Setting the Function