Q: What causes the transmission to jerk when coming to a stop, only when engine is on 2009 Hyundai Sonata

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When approaching a stop or slow down yield, the car transmission seems to jerk as it downshift.
(4) Answers
A transmission specialist will need to test drive and diagnose the issue. Low and/or dirty transmission fluid could cause this, but internal problems could also be at hand.
I found out that I needed motor mounts to correct this problem of the jerking. I replace all 4. I ordered them( ONLINE through ROCKAUTO) and I won't go into another retail store again for parts. You can't beat their prices.
Same issue with my 09 Sonata as well. This and tightening of the steering wheel when turning are why I want to trade it so bad and not go back to Hyundai, but don't want another car payment.
I have the same problem with my 2009 Sonata. It started last year at the beginning of cold season here in the middle east. It disappeared when summer came and now it started again last month when winter began. It does the jerking when down shifting from 4th to 3rd gear. My temporary solution is to shift to manual gear when slowing down, then shift back to automatic when accelarating again.