Question

a purple 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?

Answer 1

The B represents the gene for flower color.
A capital B is purple color.
A normal b is white color
Take a look at this Punett square:


The B being a capital means that it is dominant, so in this case purple is dominant.
The normal be means that its recessive. white is resessive.
So if the new plant gets a gene from the mother and father plant, 3 expressions can occur.
BB = purple (2x purple gene)
Bb = purple since capital B is dominant over normal b
bb = white

recessive genes only come to expression when they are homozygous, homozygous means 2 of the same genes so bb
dominant genes always come to expression in either homozygous or heterozygous (Bb)

So according to the diagram there's a 75% chance the new flower will be purple and 25% chance the flower will be white.

Now about your case. If you combine a purple flower (BB or Bb) with a white flower (bb) you can redraw the punett square like this:

So in the case that the purple flower is homozygous (BB) all the offspring flowers will be purple. If the purple flower is heterozygous, 50% of the offspring flower will be white.

I hope this helped.