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In the season five episode Crusaders of the Lost Mark, Applejack tells Apple Bloom after she receives her cutie mark, "If Mom and Dad were here, they'd be so proud of ya."
In the season seven episode "A Royal Problem", Applejack's parents briefly appear in a dream bubble holding an infant Applejack while Princess Celestia observes ponies' dreams.
In "The Perfect Pear", the Apples' parents' love story is revealed and detailed through flashbacks. When they were infants, Bright McIntosh of the Apple family met and became friends with Pear Butter of the rivaling Pear family, nicknaming her Buttercup. As they grow up together, their friendship slowly turns into mutual romantic affection, despite the disapproval of Bright Mac's mother Granny Smith and Pear Butter's father Grand Pear.
When the escalating feud between the Apple and Pear families threatens to split Bright Mac and Pear Butter apart, they have a secret wedding officiated by Mayor Mare. Granny Smith and Grand Pear soon find out about their marriage, and when Pear Butter's father refuses to accept her love for Bright Mac, she renounces her family ties to be with the Apples. Bright Mac and Pear Butter's eventual fate is unknown, but their legacy lives on through Applejack's honesty, Big Mac's humility, Apple Bloom's desire to help others realize their special talents, and a large tree that grows both apples and pears.
Other depictions
In Applejack and the Honest-to-Goodness Switcheroo, Applejack's mother is mentioned, though not by name, when Granny Smith gives Applejack a notebook that used to belong to Applejack's mother.
Trivia
Pear Butter's nickname is the same as the name of Buttercup and was previously used as the name of a G2 Earth pony.
In December 2011, Lauren Faust mentioned that the whereabouts of Applejack's parents had not been planned and that the show was unlikely to mention that they've passed away.
Faust stated that while she wanted it to be the case, she "didn't think they would allow it."
At the 2016 Middle Equestrian Convention in Poland, My Little Pony character designer Kora Kosicka stated in response to a fan question that Applejack's parents are dead.