Awoman with liddle syndrome has a child with a normal male. what is the probability that their child will have the syndrome?

An autosomal dominant gene is one that occurs on an autosomal (non-sex determining) chromosome. As it is dominant, the phenotype it gives will be expressed even if the gene is heterozygous.  

The chances of an autosomal dominant disorder being inherited are 50% if one parent is heterozygous (NL) for the mutant gene and the other is homozygous for the normal (NN), or 'wild-type', gene. This is because the offspring will always inherit a normal gene from the parent carrying the wild-type genes, and will have a 50% chance of inheriting the mutant gene from the other parent. If the mutant gene is inherited, the offspring will be heterozygous for the mutant gene, and will suffer from the disorder. If the parent with the disorder is homozygous for the gene, the offspring produced from mating with an unaffected parent will always have the disorder.  

Explanation:

complete the square on the right side of the equation;

-5(x + 0)^2 + 15

answer: d. y = -x^2 + 15

genetic variation can be caused by mutation (which can create entirely new alleles in a population), random mating, random fertilization, and recombination between homologous chromosomes during meiosis (which reshuffles alleles within an organism's offspring).