How should a lifeguard respond if a child is reported missing?

When a child is reported missing, it is crucial for a lifeguard to act quickly and efficiently. Alerting other lifeguards, initiating a search, and notifying management is the appropriate response because it ensures that a coordinated effort begins immediately. The presence of multiple lifeguards increases the chances of locating the child quickly, as they can cover more ground and perform a thorough search of the area. Notifying management is also essential, as they can provide additional resources, communicate with the child’s guardians, and coordinate with local authorities if necessary.

A quiet search without alerting others can lead to confusion and delays, limiting the effectiveness of the search efforts. While a public announcement might seem helpful, it could also create unnecessary panic and distract from the search. Waiting before taking action directly compromises the child's safety, as every passing moment is critical in such situations. Therefore, the proactive and comprehensive approach described in the correct answer is the most effective response in a missing child scenario.