Recall that an sp\(\textsuperscript{2}\) hybridized atom has three sp\(\textsuperscript{2}\) hybrid orbitals and one unhybridized p orbital.
The three sp\(\textsuperscript{2}\) hybrid orbitals form sigma (\(\sigma\)) bonds or hold lone pairs, depending on the atom's bonding environment.
The remaining unhybridized p orbital is oriented perpendicular to the plane of the sp\(\textsuperscript{2}\) orbitals and can overlap with another p orbital to form a pi (\(\pi\)) bond.
Therefore, an sp\(\textsuperscript{2}\) hybridized atom can form exactly one \(\pi\) bond due to the single unhybridized p orbital available for pi bonding.
Summarizing, the number of \(\pi\) bonds formed by an sp\(\textsuperscript{2}\) hybridized atom is 1.