From the Super Mario Wiki
The Mother Penguin is a penguin who appears in Super Mario 64 and in Super Mario 64 DS in Cool, Cool Mountain. She has lost her daughter, Tuxie, so Mario goes to look for her. Once Tuxie is rescued, the Mother Penguin rewards Mario with a Power Star.
If Tuxie is taken back after being delivered to the Mother Penguin, she follows Mario with a cross expression until he drops Tuxie again. However, she does not seem to react in any way if Mario gets far enough away or drops Tuxie off the edge.
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