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.