"reached its apogee" is correct and usable in written English.
You could use it to indicate that a peak or highest point was reached. An example sentence would be: "The popularity of the show reached its apogee when it won several Emmy awards."
It happened this season with "Lost," and it reached its apogee on Sunday in an episode that was largely a pleasant, nostalgic wallow for the show's fans.
It reached its apogee in Swindon's "Magic Roundabout" (pictured): one large roundabout surrounded by five mini satellites.
The arc of this luminous talent, as I see it, reached its apogee toward the close of the millennium, and then partly withdrew into enigma and opacity.
It reached its apogee on the last occasion when he went over the top and hit me too hard and too often.
It sort of reached its apogee with Gaga and, of course, of the extravagance of the Dior shows and all of that.
In his view, Western literature reached its apogee in Shakespeare, and it has been downhill ever since.
However, under Brezhnev the U.S.S.R. reached its apogee in the mid-1970s: it acquired nuclear parity with the United States and was recognized as a world superpower.
Chiprovtsi's development reached its apogee in the 17th century, when it became a bustling cultural, religious and merchant centre of that part of the Balkans.
Romanticism reached its apogee between the late 1850s and the early 1870s as it divided into several branches, including Indianism and sentimentalism.
My hunch is that kleptocracy reached its apogee and is now waning in India, while in China it continues to get worse.
The wide extent of their holdings made Thibaut and his successors major feudal lords, and it was during the 12th and 13th centuries that Champagne reached its apogee.
