1. The problem statement, all variables and given/known data Problem: how do we know for sure if x is <0 for point A? Vx-t is a graph of particle's speed over time. x represents position of the particle at any given time 3. The attempt at a solution From the function that we can see on the left side of the picture we can deduce the formula for it. It should be something like v = -a(t-b)^2+c, where a,b and c are some unknown constants >0. So i attempted to use wolframalpha to plot a function similar to this: And then I took integral of this function to find the connection between x (position of the particle) and t: From this function we can see that if the constant is equal to zero, then position x of the particle at t=0 should be zero. This means that since the textbook says that at point A x<0, our constant is =/=0, but instead is a negative number. But how do they know that constant is <0 at point A? All we have is a graph of the derivate of the function of particle's position (x) over time. When we take a derivative of this, the constant turns into zero, so I don't see the way that authors used to determine whether the constant is >0, <0 or 0. Why do they state that x<0 at A then if it could actually be anything? Thanks for help!