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.