Step 1: Understanding conjugate base concept.
A conjugate base is formed when an acid loses one proton (\(H^+\)). Therefore, to find conjugate base, we simply remove one hydrogen ion from the given species.
Step 2: Identifying the given species.
Given acid is \(H_2PO_4^{-}\), which contains two hydrogen atoms attached to phosphate group. Its charge is \(-1\).
Step 3: Removing one proton.
When one \(H^+\) is removed:
\[
H_2PO_4^{-} \rightarrow HPO_4^{2-} + H^+
\]
The charge becomes more negative by one unit.
Step 4: Checking charge balance.
Original charge = \(-1\), after removing \(+1\), new charge becomes \(-2\), hence species becomes \(HPO_4^{2-}\).
Step 5: Final conclusion.
Thus, the correct conjugate base is \(HPO_4^{2-}\), formed by loss of one proton.
Final Answer:
\[
\boxed{HPO_4^{2-}}
\]