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To identify the correct graph for the function \( f(x) = x^2 - 8x + 13 \), we can analyze it using the following steps:

### 1. Vertex Form of the Quadratic
We can rewrite the quadratic \( f(x) = x^2 - 8x + 13 \) in vertex form by completing the square.

\[
f(x) = x^2 - 8x + 13
\]
First, focus on the quadratic part:
\[
x^2 - 8x = (x - 4)^2 - 16
\]
Now, add the constant term back:
\[
f(x) = (x - 4)^2 - 16 + 13 = (x - 4)^2 - 3
\]

So, the vertex of the parabola is at \( (4, -3) \).

### 2. Analyzing the Graph
- The vertex is at \( (4, -3) \), so the graph must have its minimum point at \( (4, -3) \).
- Since the leading coefficient of \( x^2 \) is positive, the parabola opens upwards.

### 3. Comparing with the Graphs
Looking at the graphs provided:
- The correct graph should have a vertex at \( (4, -3) \).
- The parabola should open upwards.

The second graph matches this description, with a vertex at \( (4, -3) \).

### Conclusion:
The correct graph is the **second one**.

Would you like further explanation or have any questions?

Here are 5 related questions for more practice:
1. How do you complete the square for a general quadratic expression?
2. How can you find the axis of symmetry of a parabola?
3. What does the discriminant tell you about the nature of the roots of a quadratic function?
4. How does the coefficient of \( x^2 \) affect the shape of the parabola?
5. How do you convert a quadratic from standard form to vertex form?

**Tip:** Always verify the vertex of a parabola to ensure it matches the graph you're analyzing.

Identify the graph of f(x) = x^2 - 8x + 13.

Learn how to identify the graph of the quadratic function f(x) = x^2 - 8x + 13. This involves completing the square to determine the vertex and using key concepts in quadratic graphing. Suitable for students in Grades 9-11.

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