This same rock is thrown and it follows the path modeled by the function: h(t) = −16t^2 + 50t + 20

Answer 1

To find the maximum height reached by the rock, we need to find the vertex of the parabolic function h(t) = -16t^2 + 50t + 20.

The formula for finding the vertex of a parabolic function in the form of h(t) = at^2 + bt + c is given by:
t = -b / 2a

In this case, a = -16 and b = 50. Plugging these values into the formula:
t = -50 / 2(-16)
t = -50 / -32
t = 1.5625

Now that we have found the time value t at which the maximum height is reached, we can substitute this value back into the function h(t) to find the maximum height:
h(1.5625) = -16(1.5625)^2 + 50(1.5625) + 20
h(1.5625) = -16(2.4414) + 78.125 + 20
h(1.5625) = -39.0624 + 78.125 + 20
h(1.5625) = 59.0626

Therefore, the maximum height reached by the rock is approximately 59.06 feet.