need to know the answer to that question. that is a question on my homework and i don't know the answer and can't find it in my math book
Symbols were indeed introduced for convenience reasons. Because of them we can write math and perform computations on paper much faster than if we had to use words. Try writing the quadratic formula or the law of cosines entirely in words and you will see if your friends can figure out what the resulting sentences mean. They will likely be confused for a while.
As for the reasons for particular symbols, to make them easy to remember. For example = was chosen for equals because the two lines in it are of equal length, while the symbol used for square roots is a modified version of the letter r which is the first letter in the term radical which refers to nth roots.