Final answer:
The maximum height the rocket will reach is found using the vertex of the function h(s)=-3(s-1)² + 48, which indicates a maximum height of 48 feet because it's a downward opening parabola and the vertex represents the peak height.
Step-by-step explanation:
The question involves finding the maximum height that a rocket will reach based on the given function h(s)=-3(s-1)² + 48, where h is the height in feet and s is the time in seconds. We can determine the maximum height of the rocket without using calculus because the function provided is a parabola in vertex form, and the vertex of the parabola in this form gives the maximum or minimum value of the function, depending on whether the parabola opens upward or downward.
In this case, since the coefficient of the squared term is negative (-3), the parabola opens downward, which means the vertex will give the maximum height of the rocket. The vertex occurs at s=1, as can be seen directly from the equation. Substituting s=1 into the equation gives us h(1) = -3(1-1)² + 48, which simplifies to h(1) = 48. Therefore, the maximum height that the rocket will reach is 48 feet.