1. **State the problem:** We need to analyze the function $f(x) = -(x + 1)^2 + 2$ and identify its graph, vertex, and axis of symmetry. 2. **Recall the vertex form of a quadratic function:** $$f(x) = a(x - h)^2 + k$$ where $(h, k)$ is the vertex and $a$ determines the direction of the parabola (up if $a > 0$, down if $a < 0$). 3. **Identify the vertex and direction:** Given $f(x) = -(x + 1)^2 + 2$, rewrite as $f(x) = -(x - (-1))^2 + 2$. - Vertex is at $(-1, 2)$. - Since $a = -1 < 0$, the parabola opens downward. 4. **Axis of symmetry:** The axis of symmetry is the vertical line through the vertex, so: $$x = -1$$ 5. **Match with given graphs:** - Graph C is a parabola opening downward with vertex at $(-1, 2)$. - This matches our function exactly. **Final answers:** - The graph of $f(x)$ is Graph C. - The vertex is $(-1, 2)$. - The axis of symmetry is $x = -1$.