The function provided is:

\[
f(x) = -x^2 - 1
\]

### Detailed Analysis:

1. **Type of Function**: This is a **quadratic function** in the general form \( f(x) = ax^2 + bx + c \), where:
   - \( a = -1 \),
   - \( b = 0 \), and
   - \( c = -1 \).

2. **Shape and Direction**: Since \( a = -1 \), the parabola opens **downwards**. A negative coefficient for \( x^2 \) means the parabola is "upside down."

3. **Vertex of the Parabola**: The vertex can be found using the vertex formula:

   \[
   x = -\frac{b}{2a}
  

Explore the properties of the quadratic function f(x) = -x^2 - 1, including its downward-opening parabola, vertex, and how it fits into algebraic concepts. Ideal for students in Grades 9-11.

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