This research examined the nature of parent-child conversations at an informal science education center housed in an active gravitational-wave observatory. Each of 20 parent-child dyads explored an interactive exhibit hall privately, without the distraction of other visitors. Parents employed a variety of strategies to support their children's understanding of unfamiliar topics, including describing evidence, giving direction, providing explanation, making connections, and eliciting predictions. Parents' education was associated with both the amount of time dyads spent exploring exhibits and the proportion of exhibits at which parents made connections to prior experiences. Parents' attitudes toward science were likewise associated with the proportion of exhibits visited. Parent-child dyads spent more time at exhibits that encouraged Active Prolonged Engagement (APE). Parents elicited predictions more often at APE exhibits, and children described evidence and gave direction more often at APE exhibits. Thus, both participant characteristics and exhibit qualities were found to contribute to parent-child interactions in an informal science setting. (Contains 3 tables and 1 footnote.)