A particle moves in the \(xy\)-plane starting from the origin at time \(t = 0\). The position of the particle as a function of time is given by \(x(t) = \alpha t^2\) and \(y(t) = \beta t - \gamma t^2\), where \(\alpha\), \(\beta\), and \(\gamma\) are positive constants. Which of the following graphs best represents the trajectory of the particle in the \(xy\)-plane for \(t \ge 0\)?