The root word graph means to
speak
draw
write
read

Draw

The root word for educator is educate which means to teach, to train or to supervise a practice by formal instruction to develop skills, profession or trade.

The suffix -or is a word ending added to the stem of a word educate. Suffixes and prefixes are affixes or  word endings that can change or add a meaning to the stem of a word being added to. For instance, the word educate. The term "educate" is a verb meaning to teach, but when added by the suffix -or, the verb becomes a noun. It becomes "educator" which now, has a new meaning, a teacher. The difference brought by adding an affix to a stem of word is very obvious.