Trajectory high point A stone is launched vertically upward from a cliff 192 ft above the ground at a speed of 64 ft/s. Its height above the ground t seconds after the launch is given by s = -16t² + 64t + 192, for 0 ≤ t ≤ 6. When does the stone reach its maximum height?

Verified step by step guidance

1. Identify the height function given by s(t) = -16t² + 64t + 192, which is a quadratic function in the standard form s(t) = at² + bt + c.
2. Recognize that the maximum height of a quadratic function occurs at the vertex. For a quadratic in the form s(t) = at² + bt + c, the t-coordinate of the vertex can be found using the formula t = -b/(2a).
3. In this case, identify the coefficients: a = -16 and b = 64.
4. Substitute the values of a and b into the vertex formula to find the time t at which the maximum height occurs: t = -64/(2 * -16).
5. Calculate the value of t to determine when the stone reaches its maximum height, ensuring that the result falls within the given interval 0 ≤ t ≤ 6.