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The given graph is a parabola that opens downward, with its vertex at the point \((5, 4)\). Based on this, we can deduce the equation of the parabola in vertex form, which is:

\[
f(x) = a(x - h)^2 + k
\]

Where:
- \((h, k)\) is the vertex of the parabola.
- \(a\) determines the direction and width of the parabola. If \(a\) is negative, the parabola opens downward.

In this case:
- The vertex is \((5, 4)\), so \(h = 5\) and \(k = 4\).
- Since the parabola opens downward, \(a\) must be negative. The standard choice for a downward-opening parabola is \(a = -1\).

Thus, the equation becomes:

\[
f(x) = -(x - 5)^2 + 4
\]

This matches the second option in the list.

### Answer:
The correct function is:
\[
\boxed{f(x) = -(x - 5)^2 + 4}
\]

Would you like a more detailed explanation? 

Here are 5 related questions for practice:
1. How do you find the vertex form of a quadratic equation from a graph?
2. What role does the sign of \(a\) play in the graph of a parabola?
3. How would the graph change if the value of \(a\) were positive?
4. How do you complete the square to convert a quadratic equation into vertex form?
5. What is the effect of changing the values of \(h\) and \(k\) in the vertex form equation?

**Tip**: Remember that in vertex form, \((h, k)\) is always the vertex of the parabola, and the sign inside the parentheses is opposite to the vertex's x-coordinate.

¿Cuál función representa a la siguiente gráfica?

Learn how to identify a quadratic function from a parabola graph. This example involves recognizing the vertex form of the equation, understanding the direction of the parabola, and interpreting the vertex coordinates. Suitable for students in Grades 8-10.

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