Eye color is determined by genetic combination. Let R represent the gene for brown eyes and l represent the gene for blue eyes. Any gene combination including R represents browns eyes. Consider the offspring of a parents with homozygous brown-eyed, RR, gene combo and a parent with heteroz brown eyed, Rl, gene combo.

1. Show how you could use a polynomial to model the possible genetic combos of the offspring.

2. What percent of the possible genetic combos result in brown-eyed offspring?

3. What percent of the possible genetic combos are carriers for the blue-eyed gene?

4. Fill out a Punnett square to show your conclusions.

1. To model the possible genetic combinations of the offspring, we can use a polynomial expression. Let's consider using the FOIL method to multiply the two gene combinations: (RR + Rl)(RR + Rl).

Expanding this expression using the FOIL method, we get:
RR * RR + RR * Rl + Rl * RR + Rl * Rl

Simplifying further, we have:
RR^2 + 2RR * Rl + Rl^2

This polynomial expression represents the possible genetic combinations of the offspring.

2. To determine the percentage of possible genetic combinations resulting in brown-eyed offspring, we need to identify the number of combinations containing the gene for brown eyes (R). In this case, both parents have the gene for brown eyes.

From the polynomial expression, we can see that the combinations contributing to brown-eyed offspring are RR^2 and 2RR * Rl. The RR^2 combination represents homozygous brown-eyed offspring, while the 2RR * Rl combination represents heterozygous brown-eyed offspring.

Therefore, we have two combinations out of four possibilities that result in brown-eyed offspring. This means that 50% of the possible genetic combinations will result in brown-eyed offspring.

3. To determine the percentage of possible genetic combinations that are carriers for the blue-eyed gene (Rl), we need to identify the number of combinations containing the gene for blue eyes (Rl) without having brown eyes (RR).

From the polynomial expression, we can see that the Rl^2 combination represents individuals with blue eyes. However, the combinations RR^2 and 2RR * Rl contribute to brown eyes.

Therefore, we have only one combination (Rl^2) out of four possibilities that represents carriers for the blue-eyed gene. This means that 25% of the possible genetic combinations are carriers for the blue-eyed gene.

4. The Punnett square can be filled out as follows:

| R | Rl |
-------------------------
R | RR | RRl |
-------------------------
Rl | RRl | Rl^2 |

In the Punnett square, the possible genetic combinations of the offspring are represented by the intersection of the parent's genetic combinations. Each square represents a 25% chance of occurring.

The top-left square (RR) represents offspring with homozygous brown eyes (brown-eyed).
The top-right and bottom-left squares (RRl and RRl) represent offspring with heterozygous brown eyes (brown-eyed).
The bottom-right square (Rl^2) represents offspring with blue eyes (carrier for the blue-eyed gene).

This Punnett square demonstrates the possible genetic combinations and their corresponding eye colors for the offspring.

1. To model the possible genetic combinations of the offspring, we can use a polynomial. In this case, we can start by representing the parent with the homozygous brown-eyed gene combo (RR) as (R+0)^2, where the exponents indicate that both alleles are the same. Similarly, we can represent the parent with the heterozygous brown-eyed gene combo (Rl) as (R+l).

To determine the possible genetic combinations of the offspring, we can multiply these polynomials together: (R+0)^2 * (R+l). Expanding this expression, we get: R^3 + R^2l.

2. To determine the percentage of possible genetic combinations resulting in brown-eyed offspring, we need to identify the terms in the polynomial that correspond to brown eyes (represented by the R gene). In this case, the terms are R^3 and R^2l.

The term R^3 represents the possibility of having brown-eyed offspring while both parents pass on the dominant R gene. The term R^2l represents the possibility of having brown-eyed offspring while one parent passes on the dominant R gene and the other passes on the recessive blue-eyed gene l.

Thus, the percentage of possible genetic combos resulting in brown-eyed offspring is determined by these two terms.

3. To determine the percentage of possible genetic combinations that are carriers for the blue-eyed gene, we need to identify the terms in the polynomial that correspond to carrying the recessive blue-eyed gene (represented by the l gene). In this case, the term is R^2l.

The term R^2l represents the possibility of carrying the recessive blue-eyed gene while one parent passes on the dominant R gene and the other passes on the recessive blue-eyed gene l.

Thus, the percentage of possible genetic combos that are carriers for the blue-eyed gene is determined by this term.

4. We will now fill out a Punnett square to illustrate the genetic combinations:

R R
-------------
R | RR RR
|
l | Rl Rl

Based on the Punnett square, we can conclude the following:

- All offspring will have at least one dominant R gene, resulting in brown eyes.
- 75% of the offspring will have homozygous brown-eyed gene combos (RR).
- 25% of the offspring will have heterozygous brown-eyed gene combos (Rl).
- 100% of the offspring will be carriers for the recessive blue-eyed gene (l), as they all have at least one l gene present.