A Problem I Was Considering But Seems So Simple

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A ball is thrown up in the air and the speed of the ball at the second second is equal to the speed of the ball after the third second. But what would be the velocity of the ball when the time equals zero.

I have been thinking about this a lot and I'm certain that there are two answers (and I think one is negative)
 

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Show how you solved it. (A negative initial velocity wouldn't get you very far.)

Hint: Use symmetry.
 
Another hint: The speeds are equal.
 

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