Which case is noted for establishing the legal basis for racial segregation?

Plessy v. Ferguson is significant because it established the legal precedent for racial segregation in the United States through the doctrine of "separate but equal." This 1896 Supreme Court case arose when Homer Plessy, who was of mixed race, challenged Louisiana's segregation laws by refusing to leave a whites-only railroad car. The Court's ruling upheld the constitutionality of racial segregation laws, asserting that as long as the separate facilities for the races were equal, segregation did not violate the 14th Amendment's Equal Protection Clause. This decision provided a legal framework that allowed segregation to be perpetuated for decades, leading to widespread discrimination and the entrenchment of Jim Crow laws in the southern states.

In contrast, the other cases listed address different legal issues—Brown v. Board of Education focused on desegregating public schools, Marbury v. Madison established the principle of judicial review, and Roe v. Wade dealt with the legality of abortion. Each has its own historical significance but does not pertain directly to establishing the rationale for racial segregation like Plessy v. Ferguson does.