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The problem asks for the translation of the equation \( y = x^2 + 6x - 2 \) by the vector \( (0, 4) \).

### Translation of a Function

A translation by the vector \( (0, 4) \) means:
- The \( x \)-coordinate remains unchanged because the horizontal component is 0.
- The \( y \)-coordinate is increased by 4 because the vertical component is 4.

For the function \( y = x^2 + 6x - 2 \), applying a vertical translation of 4 units means adding 4 to the entire equation:

\[
y' = y + 4 = (x^2 + 6x - 2) + 4
\]

Simplifying this:

\[
y' = x^2 + 6x - 2 + 4 = x^2 + 6x + 2
\]

### Conclusion

The translated equation is \( y = x^2 + 6x + 2 \), which corresponds to option **D**.

Would you like more details or have any further questions?

Here are 5 related questions for practice:
1. How would the graph of \( y = x^2 + 6x - 2 \) change with a translation of \( (2, 0) \)?
2. What is the effect of a translation by \( (0, -3) \) on the same equation?
3. How do horizontal translations differ from vertical translations in general?
4. How can you identify translations in the graph of a quadratic function?
5. How would the vertex of the function \( y = x^2 + 6x - 2 \) be affected by this translation?

**Tip:** Always apply translations to the whole equation. For vertical translations, just adjust the constant term!

Tentukan translasi dari garis k dengan persamaan y = x^2 + 6x - 2 oleh (0, 4).

Learn how to translate the quadratic equation y = x^2 + 6x - 2 vertically by the vector (0, 4). This problem covers key algebraic concepts related to quadratic functions and translations. Suitable for students in Grades 8-10.

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