How to determine how many times a function will cross the x axis?

Usually a good indicator of how many solutions or zeros a function has is through the highest degree of the equation. A quadratic equation (usually) has 2 roots and that defines the number of times it might cross the x axis. The higher the degree, the more times the function should cross. It is however, possible for some of the zeros to be a complex solution. 

Hope I helped :)