Determine the genotype of the purple flower if purple (P) is dominant and white (p) is recessive

The question is about a test cross. Definition of a test cross: Generally a cross involving a homozygous recessive individual. When a single trait is being studies, a test cross is a cross between an individual with the dominant phenotype but of unknown genotype (homozygous or heterozygous) with a homozygous recessive individual. If the unknown is heterozygous, then approximately 50% of the offspring should display the recessive phenotype. If the individual is homozygous all the progeny will have the dominant phenotype. James' suggestion to use show the result of the two possible crosses with a Punnet square is a great suggestion.