It floats
A ball is floating on the surface of a deep body of water. A man shoves it so that it goes vertically downwards. Precisely 4 seconds later, it reappears on the surface.
A scientist observing this states that during the time it was underwater, its height in feet (taking the surface of the water as height 0) was given by the expression , where is the time in seconds.
Assuming the scientist is correct, what was the minimum height of the ball in feet during its underwater journey?
The answer is -20.
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5t^2-20t=5(t-2)^2-20. Since (t-2)^2 is non-negative definite for real t, therefore the height is greater than or equal to -20, so that it's minimum value is -20