find the vertex and axis of symmetry of f(x)=-(x-4)^2-6

To find the vertex and axis of symmetry of the quadratic function \( f(x) = -(x-4)^2 - 6 \):

1. **Vertex**: The function is in vertex form, \( f(x) = a(x-h)^2 + k \), where \( (h, k) \) is the vertex. Here, \( a = -1 \), \( h = 4 \), and \( k = -6 \). Thus, the vertex is:
   \[
   (4, -6)
   \]

2. **Axis of Symmetry**: The axis of symmetry for a quadratic function in vertex form is given by the line \( x = h \). Therefore, the axis of symmetry is:
   \[
   x = 4
   \]

### Summary:
- **Vertex**: \( (4, -6) \)
- **Axis of Symmetry**: \( x = 4 \)

Do you want more details or have any questions? Here are some related questions you might consider:

1. How do you derive the vertex form from standard form?
2. What are the characteristics of the graph of this quadratic function?
3. How would you find the y-intercept of this function?
4. Can you explain how the value of \( a \) affects the graph?
5. What are the applications of quadratic functions in real life?

**Tip**: Always check the sign of \( a \) to determine whether the parabola opens upwards or downwards.

Discover how to find the vertex and axis of symmetry of the quadratic function f(x) = -(x-4)^2 - 6. This solution includes step-by-step guidance on identifying the vertex at (4, -6) and the axis of symmetry at x = 4. Perfect for students in Grades 7-9.

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