1. **State the problem:** We are given the quadratic function $$p(x) = (x - 1)^2 - 1$$ and asked to graph it. 2. **Recall the vertex form of a quadratic function:** $$p(x) = a(x - h)^2 + k$$ where $(h, k)$ is the vertex of the parabola and $a$ determines the direction and width. 3. **Identify the vertex and direction:** Here, $a = 1 > 0$, so the parabola opens upward. The vertex is at $(h, k) = (1, -1)$. 4. **Axis of symmetry:** The vertical line through the vertex is $x = 1$. 5. **Plot key points:** - Vertex: $(1, -1)$ - Choose points around the vertex, e.g., $x=0$: $$p(0) = (0 - 1)^2 - 1 = 1 - 1 = 0$$ - $x=2$: $$p(2) = (2 - 1)^2 - 1 = 1 - 1 = 0$$ 6. **Sketch the parabola:** Plot points $(0,0)$, $(1,-1)$, $(2,0)$ and draw a smooth curve opening upward. **Final answer:** The graph of $$p(x) = (x - 1)^2 - 1$$ is a parabola with vertex at $(1, -1)$, opening upward, symmetric about $x=1$.