The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.

Question

After how many seconds does the object reach its maximum height?

2 seconds
3 seconds
6 seconds
9 seconds

Answer 1

To find the time at which the maximum height is reached for the function \( h(t) = -16t^2 + 96t + 6 \), we can use the vertex formula for a quadratic function of the form \( h(t) = at^2 + bt + c \). The time \( t \) at which the maximum height occurs is given by

\[ t = -\frac{b}{2a} \]

For our function, \( a = -16 \) and \( b = 96 \). Plugging in these values:

\[ t = -\frac{96}{2 \times -16} = -\frac{96}{-32} = 3 \]

Thus, the object reaches its maximum height after 3 seconds.

So the correct answer is 3 seconds.