Final answer:
To find the maximum height attained by an object thrown upward with an initial velocity, the peak of the projectile's parabolic trajectory is calculated from the height equation, resulting in a maximum height of 1568 feet.
Step-by-step explanation:
The maximum height attained by an object thrown upward with an initial velocity can be found by analyzing the equation for the object's height over time, h = 448t - 32t², where h is the height in feet and t is the time in seconds. To find the maximum height, we must determine the vertex of the parabolic function, which represents the peak of the projectile's trajectory. Since the equation is in the form of h(t) = at² + bt + c, where a = -32 and b = 448, the time at which the maximum height occurs is given by t = -b/(2a).
Substituting the values in gives t = -448/(2*(-32)) = 448/64 = 7 seconds. Now, we calculate the maximum height by substituting t = 7 back into the original equation: h = 448*7 - 32*7². Simplifying this gives us h = 3136 - 1568 = 1568 feet as the maximum height.
Therefore, the maximum height attained by the object is 1568 feet.