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The given function is a quadratic equation in the form \( f(x) = x^2 - 25 \). 

To identify the vertex and axis of symmetry:

1. **Vertex of a quadratic in the form \( f(x) = ax^2 + bx + c \):** The formula for the x-coordinate of the vertex is \( x = -\frac{b}{2a} \). Here, \( a = 1 \) and \( b = 0 \), so:

   \[
   x = -\frac{0}{2 \times 1} = 0.
   \]

2. **Find the y-coordinate:** Substitute \( x = 0 \) into the function to find the y-coordinate of the vertex:

   \[
   f(0) = 0^2 - 25 = -25.
   \]

   Therefore, the vertex of the function is \( (0, -25) \).

3. **Axis of symmetry:** The axis of symmetry for a quadratic function is the vertical line that passes through the x-coordinate of the vertex. Since the x-coordinate is 0, the axis of symmetry is:

   \[
   x = 0.
   \]

### Summary
- The vertex of the function is \( (0, -25) \).
- The axis of symmetry is the line \( x = 0 \).

Would you like more details or have any questions?

### Related Questions
1. How do you find the vertex of a quadratic function in standard form?
2. What does the axis of symmetry represent in a parabola?
3. How does the coefficient of \( x^2 \) affect the direction of the parabola?
4. What are the steps to rewrite a quadratic function in vertex form?
5. How can the vertex form of a quadratic equation be useful in graphing?

**Tip:** The vertex form of a quadratic equation is \( f(x) = a(x-h)^2 + k \), where \( (h, k) \) is the vertex. This form makes it easier to identify the vertex directly.

Identify the vertex and the axis of symmetry for the function: f(x) = x^2 - 25

Learn how to identify the vertex and axis of symmetry for the quadratic function f(x) = x^2 - 25. The vertex is at (0, -25) and the axis of symmetry is x = 0. This guide covers essential algebraic concepts, suitable for Grades 9-11.

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