Final answer:
The Missouri Compromise and the Compromise of 1820 were two legislative actions aimed at preserving the Union by balancing interests of slave and free states.
Step-by-step explanation:
The two actions by the federal government that were attempts to preserve the Union in the face of a bitter quarrel over slavery were D) Missouri Compromise and Compromise of 1820. The Missouri Compromise was an agreement passed in 1820 between the pro-slavery and anti-slavery factions in the United States Congress, involving primarily the regulation of slavery in the western territories. It prohibited slavery in the former Louisiana Territory north of the parallel 36°30' north except within the boundaries of the proposed state of Missouri. Later, the Compromise of 1850 was another attempt which included several laws aimed at appeasing both sides, such as admitting California as a free state and establishing a stronger Fugitive Slave Act.