1. **Problem statement:** Graph the circle given by the equation $$(x + 1)^2 + y^2 = 81$$. 2. **Identify the center and radius:** This is the equation of a circle in standard form $$(x - h)^2 + (y - k)^2 = r^2$$ where the center is $$(h,k)$$ and the radius is $$r$$. 3. From the equation, we see: - Center $$= (-1, 0)$$ (because $x + 1 = x - (-1)$) - Radius $$r = \sqrt{81} = 9$$ 4. **Graph description:** - The circle is centered at $$(-1, 0)$$ - It intersects the x-axis where $$y = 0$$: $$ (x+1)^2 = 81 \implies x+1 = \pm 9 \implies x = -10 \text{ or } 8 $$ - It intersects the y-axis where $$x = 0$$: $$ (0+1)^2 + y^2 = 81 \implies 1 + y^2 = 81 \implies y^2 = 80 \implies y = \pm \sqrt{80} \approx \pm 8.944 $$ 5. The circle can therefore be drawn on a coordinate plane with the x-axis and y-axis ranging approximately from $$-10$$ to $$9$$ and $$-9$$ to $$9$$ respectively, centered at $$(-1,0)$$ with radius $$9$$. 6. **Final answer:** The graph represents a circle centered at $$(-1,0)$$ with radius $$9$$, matching the equation $$(x + 1)^2 + y^2 = 81$$.