When writing a persuasive essay, it is important to structure your essay with valid points, beginning with the strongest and moving to the others. Usually three strong points are sufficient, along with rebuttals of possible arguments against these points. Now, regarding your examples from The Simpsons, it is worthy of note that your arguments about the support of violence in this animated show are not really valid ones because this show is intended for adult audiences, not youthful ones, and the show is predicated upon satire. That is, the acts of violence, etc., by Homer and Bart are subjects of satire, and therefore employed to ridicule adult behavior, not support violence.
You will be better served if you research violence in television and find other television programs that suggest that violence is appropriate or even necessary in certain circumstances. Find studies and statistics that you can report as support for this essay. Statistics and statements from authorities, also, are viable support. For instance, you will want to include something like this,
A University of Michigan researcher in 2003 demonstrated that watching violent media can affect willingness to help others in need......Desensitization can reduce the perception of the seriousness of injury....
Then quote from the researcher his findings. Use several sources for support to demonstrate that you have well explored the topic. The more documentation you use, the more you will demonstrate that you have researched your topic.
Below is a link to assist you in the revising of your argumentative essay.