If I have Applied Researchers empower and play Shock blast is it free?

It depends on Shock Blast's printed cost — you pay its cost minus 3 (Shock Blast's own −2 plus Applied Researchers' −1), to a minimum of 0. So it's free if the printed cost is 3 or less; if it costs more, you pay the difference.

Two notes: Applied Researchers' "to a minimum of [1]" only constrains her own discount — Shock Blast's −2 can still take the cost to 0 (apply her discount first for the best result, Rule 356.4.d–e). And once she's Empowered, she satisfies "if you control something empowered" for Shock Blast's own condition. She also knocks 1 [A] off the Power cost. One caveat: "Shock Blast" isn't in my card database, so this assumes the −2 condition text you quoted (FAQ #11897).