1. **State the problem:** We need to sketch the graph of the equation $$y^2 = 1 - x$$. 2. **Rewrite the equation:** To understand the graph better, solve for $y$: $$y = \pm \sqrt{1 - x}$$. 3. **Domain considerations:** Since the expression under the square root must be non-negative, $$1 - x \geq 0 \implies x \leq 1$$. 4. **Shape and symmetry:** The graph is symmetric about the x-axis because $y$ is squared. 5. **Intercepts:** - When $x = 0$, $y = \pm \sqrt{1} = \pm 1$. - When $y = 0$, $1 - x = 0 \implies x = 1$. 6. **Graph description:** The graph is a sideways parabola opening to the left with vertex at $(1,0)$. 7. **Final answer:** The graph of $$y^2 = 1 - x$$ is a parabola opening left with vertex at $(1,0)$ and domain $x \leq 1$.