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The problem asks you to evaluate the expression \( x^2 + 8x + 4 \) when \( x = -6 \).

Let's solve it step by step:

1. Start with the expression: 
   \[
   x^2 + 8x + 4
   \]

2. Substitute \( x = -6 \):
   \[
   (-6)^2 + 8(-6) + 4
   \]

3. Now calculate each part:
   - \( (-6)^2 = 36 \)
   - \( 8 \times (-6) = -48 \)
   - The constant \( +4 \) remains as is.

4. Now combine everything:
   \[
   36 - 48 + 4 = -12 + 4 = -8
   \]

So, the value of the expression when \( x = -6 \) is **-8**.

Let me know if you need more details or further clarification!

### 5 Related Questions:
1. What happens if \( x = 0 \) in the same expression?
2. How would the solution change if the middle term were \( 8x \) replaced by \( -8x \)?
3. How do you solve quadratic equations like \( x^2 + 8x + 4 = 0 \)?
4. What is the significance of the discriminant in quadratic equations?
5. How does the value of \( x \) affect the shape of a quadratic function graph?

### Tip:
Always carefully apply the sign of the numbers when substituting values, especially with negative numbers.

Evaluate the expression when x = -6: x^2 + 8x + 4

Learn how to evaluate the quadratic expression x^2 + 8x + 4 when x = -6. This problem involves basic algebraic concepts such as substitution and simplifies to -8. Suitable for students in Grades 6-8.

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