WASHINGTON — The Supreme Court agreed on Monday to decide whether judges must determine that juvenile offenders are incorrigible before sentencing them to die in prison. The case, involving a teenager who killed his grandfather, is the latest in a series of cases on the constitutionality of harsh punishments for youths who commit crimes before they turn 18.

The case, Jones v. Mississippi, No. 18-1259, concerns Brett Jones, who had recently turned 15 in 2004 when his grandfather discovered his girlfriend in his room. The two men argued and fought, and the youth, who had been making a sandwich, stabbed his grandfather eight times, killing him.

In 2005, Mr. Jones was convicted of murder and sentenced to life without the possibility of parole, the mandatory penalty under state law.

In 2012, in Miller v. Alabama, the Supreme Court ruled that automatic life sentences for juvenile offenders violated the Eighth Amendment’s ban on cruel and unusual punishment. The decision repeatedly criticized mandatory sentences, suggesting that only ones in which judges could take account of the defendant’s age were permissible.