I lost my temper with my teenager yesterday. Should I apologise to him?

Yes, apologising to your child does not lower your authority; in fact it teaches him what taking responsibility means. Teenagers are very sensitive to fairness, and when you admit a mistake, he learns that owning up is a strength, not a weakness. Choose a calm moment, go to him, and state directly what you regret, for example a tone that was too harsh or an accusation made too hastily. Do not add a ‘but’ that cancels the apology. This example is far more effective than a thousand pieces of advice about character. A relationship repaired after conflict often becomes stronger than before. See educating the family.