WATCH THIS: TUESDAY

“America’s Got Talent” (7 p.m., NBC): The season’s contest moves into a new phase with the start of the live episodes ... and more specifically, the Live Quarter Finals. This first round of them is bound to have judges Mel B, Simon Cowell, Heidi Klum and Howie Mandel getting sharper in their critiques of acts that they (and, presumably, the viewing audience) have grown fond of. The results will be announced in another episode Wednesday.