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## Answers

*"An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What will be the object's maximum height? When will it attain this height?"*

The initial height is 80 feet above ground and the initial speed is 64 ft/s. Since the units are "feet", then the number for gravity will be 16, and the equation is:

s(t) = –16t2 + 64t + 80

For a negative quadratic like this, the maximum will be at the vertex of the upside-down parabola. From graphing, to find the vertex; in this case, the vertex is at (2, 144):

h = –b/2a = –(64)/2(–16) = –64/–32 = 2

k = s(2) = –16(2)2 + 64(2) + 80 = –16(4) + 128 + 80 = 208 – 64 = 144

According to the equation, plugging in time values and extracting height values, so the input "2" must be the time and the output "144" must be the height.

**It takes two seconds to reach the maximum height of 144 feet.**