Question

A rock is thrown upward from the edge of a bridge and onto a road that is 12 feet below the bridge. The function h(x) = −x^2 + 3x + 12 gives the height, h, in feet, the rock travels in x seconds from the time it was thrown. When will the rock hit the road?

A) The rock will hit the road in 4 seconds.
B) The rock will hit the road in 2 seconds.
C) The rock will not hit the road.
D) The rock will hit the road in 6 seconds.

Answer 1

The rock will hit the road after 3 seconds.

Step-by-step explanation:

To determine when the rock will hit the road, we need to find the time when the height of the rock, as given by the function h(x) = −x^2 + 3x + 12, is equal to 12 feet.

First, we set h(x) = 12 and solve for x:

−x^2 + 3x + 12 = 12

−x^2 + 3x = 0

x(3 - x) = 0

x = 0 or x = 3

The rock will hit the road after 3 seconds. Therefore, the correct answer is A) The rock will hit the road in 4 seconds.