In this experiment, the molecules in food coloring are separated by gel electrophoresis. The different dyes have different structures and the number of bands represent the number of different molecules in each dye and the distance that the dyes migrated in the gel reflects the both the size and the charge of the molecule. Smaller molecules will travel faster because they can get through the pores of the agarose more quickly, and dyes that have more negative charges will migrate more quickly in the electric field.
Your project is due tomorrow, so I know you are short of time, but if you want to explain the molecular basis of your results, you could look up the structure of each dye that you used and list the molecular weight and number of charges for each molecule to confirm your results. For example, here is a website that includes the structure of Allura Red, also known as Red Dye #40. You may have used this dye if you used red food coloring. This dye has a molecular weight of 496 and it has 3 negative charges (2 sulfonic acid (SO3-) and 1 carboxyl group (COO-)
Brilliant blue has a molecular weight of 793 and a net negative 2 charge (3 negative sulfonic acid and one positive nitrogen group), so you would expect this molecule to migrate more slowly in the electrical field compared to Allura Red.
Here is an answer for your question about yellow dye. You should look at the label of the food coloring you used and find the list of ingredients. The yellow dye may have been tartrazine, which has a molecular weight of 543 and 3 negative charges (2 sulfonic, one carboxyl). Or, it may have been a combination of two dyes. If there were two molecules used, then you should have seen two bands on your gel.
Congratulations on your win! I think your extra effort to understand the science behind this project really paid off. Thanks for letting us know. Good luck at the next level of competition!