The graph touches the x-axis at -7, since it bounces at that point and change direction. We can know the graph touches and doesn't pass through the x-axis by understanding it is a quadratic function, which always forms a parabola.
This works out at 3,628,800 possible routes. Trying one route every day in a five-day working week for 50 working weeks, it takes 14,515 years to try them all.