In the 19th century the transitive sense (1a) was prescribed; the intransitive <I graduated from college> was condemned. The intransitive prevailed nonetheless, and today it is the sense likely to be prescribed and the newer transitive sense (1b) <she graduated high school> the one condemned. All three are standard. The intransitive is currently the most common, the new transitive the least common.
Examples of GRADUATE
He graduated from the university last June.
They both graduated with honors.
She graduated with a degree in history.
He joined the navy after graduating from high school.
a graduating class of 300 students
He joined the navy after graduating high school.
The word has graduated from slang to accepted use.
My nephew has graduated from baby food to solid food.
Origin of GRADUATE
Middle English, from Medieval Latin graduatus, past participle of graduare, from Latin gradus step, degree