To find the height of the pen 3 seconds after it was dropped, substitute t=3 into the quadratic function h=-16t+250:
h=-16(3)+250
h=-48+250
h=202
The height of the pen 3 seconds after it was dropped is 202 feet.
To find the rock's maximum height above the water, we need to find the vertex of the quadratic function f(t)=-16t^2+32t+80, since the vertex represents the maximum or minimum point of a quadratic function.
The x-coordinate of the vertex is given by the formula: x = -b/2a. In this case, a=-16 and b=32, so:
x = -32/(2*(-16))
x = -32/(-32)
x = 1
To find the y-coordinate of the vertex, substitute x=1 into the quadratic function:
f(1) = -16(1)^2 + 32(1) + 80
f(1) = -16 + 32 + 80
f(1) = 96
The rock's maximum height above the water is 96 feet.
Answers & Comments
Answer:
To find the height of the pen 3 seconds after it was dropped, substitute t=3 into the quadratic function h=-16t+250:
h=-16(3)+250
h=-48+250
h=202
The height of the pen 3 seconds after it was dropped is 202 feet.
To find the rock's maximum height above the water, we need to find the vertex of the quadratic function f(t)=-16t^2+32t+80, since the vertex represents the maximum or minimum point of a quadratic function.
The x-coordinate of the vertex is given by the formula: x = -b/2a. In this case, a=-16 and b=32, so:
x = -32/(2*(-16))
x = -32/(-32)
x = 1
To find the y-coordinate of the vertex, substitute x=1 into the quadratic function:
f(1) = -16(1)^2 + 32(1) + 80
f(1) = -16 + 32 + 80
f(1) = 96
The rock's maximum height above the water is 96 feet.