Below are the motions of the Bird and the Slug.
The Slug has parametric equations x=t²-4t, y=2t+5, 0≤t≤4.
The Bird has parametric equations x=t-4, y=-t+17, 0≤t≤8.
The animation is from t=0 to t=8 seconds. You can watch the timeline below the graph. The Slug and its path disappear after t=4 when it gets eaten. The animation will repeat.