The given equation is:

\[
y = -(x - 6)^2 - 1
\]

This is a quadratic equation representing a parabola. Here's a breakdown of its key features:

1. **Vertex Form**: The equation is already in the vertex form of a parabola, which is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

2. **Vertex**: In this equation, \( h = 6 \) and \( k = -1 \). Therefore, the vertex of the parabola is at \( (6, -1) \).

3. **Direction**: The coefficient of the squared term is negative (\(a = -1\)), so the parabola opens downward.

4. **Axis of Symmetry**: The axis of symmetry is a vertical line passing through the vertex, which is \( x = 6 \).

5. **Y-intercept**: To find the y-intercept, set \( x = 0 \) and solve for \( y \):
   \[
   y = -(0 - 6)^2 - 1 = -(36) - 1 = -37
   \]
   So, the y-intercept is \( (0, -37) \).

Would you like more details on any of these points, or do you have any questions?

Here are five related questions to explore further:

1. What is the range of the function \( y = -(x - 6)^2 - 1 \)?
2. How do you find the x-intercepts of this parabola?
3. What is the domain of any quadratic function?
4. How would the graph change if the equation were \( y = (x - 6)^2 - 1 \) instead?
5. Can you derive the standard form of a quadratic equation from the vertex form?

**Tip:** Remember, the vertex form of a parabola is handy for quickly identifying the vertex and the direction in which the parabola opens.

Explore the quadratic equation y = -(x - 6)^2 - 1 and its properties. This equation is analyzed in vertex form, highlighting its vertex, direction, axis of symmetry, and y-intercept. Suitable for students studying quadratic equations and parabolas in Grades 9-12.

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