The problem is written in Dutch and can be translated as:

"Given is the function $f(x) = -x^2 + 4x$. By reflecting it over the line $y = 3$, the graph of a function $g$ is formed. Find the equation of $g$."

Solution:

1. The reflection is over the line $y = 3$, which means the function needs to be vertically reflected across this line. This can be done by subtracting the function values from $6$, since the reflection formula over $y = 3$ is given by:

$g(x) = 2 \cdot 3 - f(x) = 6 - f(x)$

2. Substitute $f(x) = -x^2 + 4x$ into this formula:

$g(x) = 6 - (-x^2 + 4x)$ $g(x) = 6 + x^2 - 4x$

Thus, the equation of the reflected function $g(x)$ is:

$g(x) = x^2 - 4x + 6$

Would you like more details on how the reflection works, or do you have any further questions?

Here are 5 related questions to expand on this topic:

1. What happens when a function is reflected over the x-axis or the y-axis?
2. How does the graph of $f(x) = -x^2 + 4x$ look before and after reflection?
3. What would the equation be if the function was reflected over a different horizontal line, such as $y = 2$?
4. How can we determine the vertex of the parabolas before and after reflection?
5. Can this method of reflection be applied to non-parabolic functions as well?

Tip: When reflecting functions over a horizontal line $y = c$, the transformation is $g(x) = 2c - f(x)$, ensuring that the vertical distances from the line are mirrored perfectly.