https://file.aiquickdraw.com/mathbot/file/1726796235867skjxymsj.jpg

The given image shows a parabolic graph with a description in Indonesian, asking for the equation of the image of \( f(x) \) under a translation \( T = (2, 3) \). We are provided with four possible answer choices for the new function \( g(x) \).

### Breakdown:
1. **Graph observation:**
   The graph represents a downward-facing parabola (suggesting a negative leading coefficient), likely centered at or near the origin.

2. **Translation details:**
   - A translation \( T = (2, 3) \) means shifting the graph:
     - Horizontally by 2 units to the right.
     - Vertically by 3 units upward.
   The translation formula for a function is:
   \[
   g(x) = f(x - h) + k
   \]
   where \( h = 2 \) and \( k = 3 \).

3. **Choices and transformations:**
   Without the exact original equation \( f(x) \), it's hard to confirm the correct option immediately. However, we can assume the general structure of the function will be affected by the translation rules.

Would you like a detailed calculation based on estimating the original function from the graph, or further elaboration on how translations affect the function's equation?

### Relative Questions:
1. What is the general form of a quadratic equation?
2. How does a horizontal translation affect the graph of a function?
3. How do we translate functions vertically and horizontally?
4. Can you calculate the vertex of a parabola from its equation?
5. What other transformations can be applied to parabolic functions?

**Tip:** When translating a graph, always ensure that the vertex or key points of the function are correctly shifted according to the given transformation.

Perhatikan grafik berikut. Persamaan bayangan f(x) oleh translasi T = (2, 3) adalah ...

Understand how to apply the translation T = (2, 3) to a quadratic equation's graph. This problem involves graph translations and algebraic manipulation of a quadratic function. Suitable for students in Grades 9-11.

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