Two parents both have the dominant phenotype for a trait. their offspring, however, exhibit the recessive characteristic. what can we assume about the genotype of the parents?

We can assume that the genotype of the parents are heterozygous. Which means they have a gene for the dominant trait and recessive trait at the same time.

This is because only recessive phenotype is shown for an individual if both of the genes are recessive. They most be homozygous recessive. Even if one dominant gene exist, their phenotype would be dominant.

Therefore, for parents to produce offsprings with only recessive genes, each of them must contain at least one recessive gene. And when the both parents shows a dominant phenotype, this means the other gene of them must be recessive. Therefore, they're heterozygous.