If parents are A and B, what are the possible genotypes of the parents? What are all the possible blood types of children? What if the parents are AB and A?

See below:

Explanation:

With analyses of this type, we say that one gene comes from Dad and one from Mom, resulting in 2 genes within a child. Some genes are dominant (meaning that if they are present, they determine that particular factor) and others are recessive (so the 2 genes in a person must be the same for that quality to win out).

Quick example - Brown eyes are dominant and blue eyes are recessive. There are 3 different ways the two genes can be: BB, Bb, bb. The first 2 have the dominant Brown gene and so that person will have Brown eyes. The last one has both genes as b and so that person will have blue eyes.

Ok - on to the question!

There are 4 blood types:
O, A, B, AB

A and B are dominant genes. O is recessive. A and B are equally dominant so that when they get together they create a new blood type: AB.

A person with blood type A can have genotype: AA, AO
A person with blood type B can have genotype: BB, BO
A person with blood type O can have genotype OO
A person with blood type AB can have genotype AB

So what happens to a child of parents with blood types AB and A? We know that the AB parent will contribute either an A gene or a B gene to the child. The A parent may have a genome of AA or AO, so potentially can contribute an A gene or an O gene. Since there is more potential variety in a child with a parent with AO, let's assume the parent is that genome. So the child can have the following genotypes (I'll use subscripts to indicate where the genes are coming from):

${A}_{A B} {A}_{A O} = \text{blood type A}$
${A}_{A B} {O}_{A O} = \text{blood type A}$
${B}_{A B} {A}_{A O} = \text{blood type AB}$
${B}_{A B} {O}_{A O} = \text{blood type B}$