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The given expression is \( y^2 + 6y + 9 \), and we are asked to evaluate it when \( y = -4 \).

### Step-by-Step Solution:

1. Substitute \( y = -4 \) into the expression:
   \[
   (-4)^2 + 6(-4) + 9
   \]

2. Evaluate each term:
   - \( (-4)^2 = 16 \)
   - \( 6(-4) = -24 \)
   - The constant term is \( 9 \).

3. Now, sum the values:
   \[
   16 + (-24) + 9 = 16 - 24 + 9 = 1
   \]

### Final Answer:
The value of the expression when \( y = -4 \) is \( \boxed{1} \).

Would you like more details or have any questions?

### Related Questions:
1. How do you evaluate quadratic expressions with different coefficients?
2. What happens when the value of \( y \) is a positive number instead of negative?
3. How can we factor the expression \( y^2 + 6y + 9 \)?
4. What is the geometric interpretation of the expression \( y^2 + 6y + 9 \)?
5. How can this problem be extended to solving quadratic equations?

### Tip:
Always double-check each step when substituting values to ensure accuracy, especially with negative signs.

Evaluate the expression when y = -4: y^2 + 6y + 9

Learn how to evaluate the quadratic expression y^2 + 6y + 9 by substituting y = -4. This problem covers core algebraic concepts, including the substitution method, and is suitable for students in Grades 7-9.

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