Final answer:
The highest point that the object reaches is calculated by finding the vertex of the parabola represented by the equation h(t) = -16t^2 + 32t + 128. Using the vertex formula, the object reaches its highest point at 1 second, with a maximum height of 144 feet.
Step-by-step explanation:
How to Find the Highest Point Reached by the Object
The student is given the quadratic equation h(t) = -16t2 + 32t + 128 to model the vertical position of an object launched from the top of a building. To find the highest point the object reaches, we look for the vertex of the parabola represented by this equation, as the vertex will give us the maximum height. The time at which this occurs is when the velocity is 0, which is the point of time before the object starts descending.
Since the quadratic term is negative (-16t2), we know the parabola opens downwards and thus the vertex represents the maximum point. The vertex can be found by using the formula t = -b/(2a), where a = -16 and b = 32. Plugging these values into the formula gives us t = -32/(2*-16) = 1 second as the time at which the object reaches the highest point.
Substituting t = 1 second back into the equation for h(t) gives us h(1) = -16(1)2 + 32(1) + 128 = 144 feet, which is the highest point reached by the object.