Final answer:
The maximum height of the golf ball hit off a 128-foot hill is 128 inches, reached at the time of 1 second after being hit.
Step-by-step explanation:
To determine the maximum height of a golf ball after it is hit off a hill, we can use the given function h(t) to model the height of the ball over time.
The function provided h(t) = -8t2 + 16t + 120 is a quadratic equation which follows the standard form of at2 + bt + c where a, b, and c are constants.
In this case, the constants are a = -8, b = 16, and c = 120. The maximum height is achieved at the vertex of the parabola represented by this function.
To find the time t at which the maximum height occurs, we use the formula t = -b/2a.
Plugging our values in, we get t = -16/(2 × -8)
= 1 second.
To find the maximum height, we substitute t back into the original equation: h(1) = -8(1)2 + 16(1) + 120
= 128 inches.
Therefore, the maximum height the golf ball reaches after being hit off the hill is 128 inches.