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Hi elizabeth, thanks for the question. The formula $v_f^2 = v_i^2 + 2ad$ is more generic than you're imagining. I think what you have in mind is that $v_f = -v_i$ at the time when the ball has returned to the thrower's hand, and that's true. But this formula works for all times when displacement is zero ($d=0$), and there's one other time when that's the case, namely, in the beginning! This "in the beginning" solution is kind of trivial since it's so obvious that the final velocity after basically no time has elapsed is the same as the initial velocity. This is what the solution $v_f = +v_i$ is telling us, that there is a moment when the final velocity is equal to the positive of the initial velocity, and it's our job to make the physical interpretation of that mathematical solution to understand that it's referring to the moment when the ball is launched. The formula gives all solutions when the displacement is zero, and there are two moments when that's the case: initial launch, and the much later return to the hand.