Answer: You can certainly cut it back to try to reinvigorate it. Make sure it receives ample water and fertilizer after you trim it. Give it sun all morning and protection from hot afternoon sun to help it recover. Also investigate the roots, yes. It may be potbound in which case repotting might help. Or, it may have suffered root damage at some point due to lack of water or to overwatering (make sure the drain holes in the pot are functioning). Good luck with your third petunia!
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