Apurple flower with an unknown genotype is crossed with a white flower how do you determine the genotype if hte purple flower if purple is dominant and white is recessive?

You have already worked out that the white flower must have genotype pp (two recessive white alleles) and that the purple flower could be homozygous (PP) or heterozygous (Pp). 

Now you need to draw Punnet squares for both possibilities and show that the way to determine the genotype is the proportion of purple offspring. If the genotype is PP, then all the progeny will inherit one P and one p, making 100% purple flowers. If the purple flower is Pp, then half will inherit P and half will inherit p, making for half white and half purple flowers in the next generation.