There’s not enough answer that question
A participial phrase contains a participle, which is a verbal form with the endings -ed or -ing (or irregular, such as "written", as in "Written on monday (the piece was famous already on Tuesday)).
here the participle is "noted" and the whole phrase is this one:
Noted for her beauty
Puritans as a political entity largely disappeared, but Puritan attitudes and ethics continued to exert an influence on American society. They made a virtue of qualities that made for economic success—self-reliance, frugality, industry, and energy—and through them influenced modern social and economic life.
d. plantations required a large work force, and slavery was a cheap and easy way to fulfill labor needs.
