I heard that a person should say all 3 paragraphs of Shema before sof z'man kriyat sh'ma if their shul starts after sof z'man kriyat sh'ma. What's the source for the need to say all three p'rakim to be yotzei?
The obligation to say all three parshiyos to fulfil the obligation of kriyas shema is found in Berachos 13a.
There is a dispute among the Rishonim if the biblical obligation requires all three parshiyos; there are many opinions defining the biblical obligation: the first verse (Ramban, Sefer HaChinuch), the first paragraph (Rashi); the first two paragraphs (Rabeinu Yona, IIRC); or all three (Rambam). [Some hold that biblically, one can fulfil the obligation with any parsha, and the institution to fulfil the obligation with these three specifically is Rabbinic in origin]
All agree, however, that there is an obligation to read all three daily.