The genotype of a hybrid plant from a cross and its determination?
Real genetics is complicated

Biology is more complicated that you seem to expect. The answer very much depends upon the underlying genetics of the trait (and the underlying non-genetic factor affecting the trait; see here) as well as the genotype you are crossing it with.

Simplified model

But let's assume an extremely simple model of pure dominance / recessivity at a single bi-allelic locus. Let a be the recessive allele and A be the dominant allele. Let's assume the pure line you are using for the crossing is homozygote for the a allele (and let assume that we know it).


If the parent is AA, then all offspring will be Aa and all will have the dominant phenotype.
If the parent is Aa, then 50% of the offspring will be Aa and have the dominant phenotype and 50% of offspring will be aa and have the recessive phenotype.
If the parent is aa, then all offspring will be aa and have the recessive phenotype.


So, under this simple model, if you can produce a high enough number of offsprings to make good statistics, then yes, looking at the F1 generation is enough to determine the genotype of the parent.

Under a more complex model, it is not necessarily possible to only look at the F1 generation.