My school goes off a semester-based approach and does not definitely give a “final grade” per se. If I were to document my final grades, would I just average my two semester grades?
For what purpose? The data on an application should basically mirror your transcript.
@skieurope For self-reporting grades on an application
How is the application set up for entry of grades?
@MWolf Course, Level, Final Grade
What do you see on your report card?
Do you see quarterly grades and a final grade?
Do you see semester grades and a final grade?
If there are any doubts ask your guidance counselor.
Presumably if the OP’s report card included a final grade, it would be easy to know what to enter as the final grade. 
My kid’s school, for instance, produces report cards and transcripts that say Class Name, Semester 1 Grade, Semester 2 Grade. The two semester grades are entirely independent of one another. There exists no concept of an overall “final grade” that any teacher or guidance counselor could advise upon.
I’d ask the program to which you’re applying, myself.
When it is time to take midterms and finals do teachers tell you how those grades are used? I know at our high school we get 4 quarterly grades, a midterm grade and final grade on report cards. The final grade also listed on the last report card comes from 20% of each quarterly grade and 10% of the midterm and final grades. That final grade is what is used for gpa after the year is over and is the grade that is on the transcript mailed to colleges. Since every school does things there own way it is a question that if isn’t answered in your school handbook may best be answered by guidance at your school.
Well, my school is on a quarter-based system, and each semester grade is 3/7 of the first quarter grade, 3/7 of the second, and 1/7 of the exam grade. The two semester grades seem independent, and I haven’t heard of any policy toward final grades. I’ll probably just email my guidance counselor, though, as the safe route.