How many energy do I have to use to play Shock Blast while I have an empowered Applied Researcher at my base? Shock Blast is a card that says "This costs [2] less if you control something empowered."

You pay Shock Blast's printed energy cost minus 3 (its own −2 plus Applied Researchers' −1), to a minimum of 0 — and Applied Researchers also removes 1 power of any domain from the cost.

The "to a minimum of [1]" on Applied Researchers only constrains its own discount (Rule 356.4.e) — it doesn't prevent Shock Blast's −2 from reducing further. Apply Applied Researchers first, then Shock Blast's discount, and you can reach 0 total (same principle as the Eager Apprentice/Sky Splitter example in Rule 356.4.e). You can't pay less than 0 energy (Rule 356.6).

One caveat: I couldn't find a card named "Shock Blast" in the card database, so this ruling is based on the text you quoted. If the printed cost differs, just subtract 3 from it using the same logic.