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We are given that the vertex of the quadratic function \( f(x) \) is \( (6, 4) \), and the new function is defined as \( g(x) = f(-x) + 2 \).

Let's break down the transformation:

1. **Reflection across the y-axis:** The term \( f(-x) \) reflects the graph of \( f(x) \) over the y-axis. This will change the x-coordinate of the vertex from 6 to -6, because reflecting over the y-axis inverts the sign of the x-coordinate.
   
2. **Vertical translation:** The \( +2 \) outside of \( f(-x) \) shifts the entire graph upwards by 2 units. This means the y-coordinate of the vertex will increase by 2 from 4 to 6.

### Vertex of \( g(x) \)
- The x-coordinate changes from 6 to -6.
- The y-coordinate changes from 4 to \( 4 + 2 = 6 \).

Thus, the new vertex of the function \( g(x) \) is \( (-6, 6) \).

Do you need any further clarifications or details?

### Related questions:
1. What is the effect of reflecting a function across the x-axis instead of the y-axis?
2. How does a vertical shift affect the graph of a quadratic function?
3. What happens to the vertex if we apply a horizontal shift instead of a vertical shift?
4. How do horizontal and vertical reflections affect the symmetry of a parabola?
5. Can you derive the general form of a quadratic function based on its vertex?

### Tip:
When transforming functions, always handle horizontal and vertical changes separately, as their effects on the graph are distinct.

A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (6, 4). What is the vertex of the function defined as g(x) = f(-x) + 2?

Explore how the vertex of a quadratic function changes with reflections and vertical shifts. In this problem, the vertex of f(x) is (6, 4), and the transformation g(x) = f(-x) + 2 moves the vertex to (-6, 6). Understand the reflection across the y-axis and vertical shifts for high school algebra students.

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