1. **Problem:** Given the circle equation $$(x+1)^2 + (y-4)^2 = 9,$$ identify the center and radius, and find its x-intercepts. 2. **Formula and rules:** The general form of a circle is $$(x-h)^2 + (y-k)^2 = r^2,$$ where $(h,k)$ is the center and $r$ is the radius. 3. **Identify center and radius:** Comparing, we see $h = -1$, $k = 4$, and $r^2 = 9$, so radius $r = 3$. 4. **Find x-intercepts:** At x-intercepts, $y=0$. Substitute $y=0$ into the equation: $$ (x+1)^2 + (0-4)^2 = 9 $$ $$ (x+1)^2 + 16 = 9 $$ $$ (x+1)^2 = 9 - 16 = -7 $$ Since the right side is negative, there are no real x-intercepts. **Final answer:** - Center: $(-1,4)$ - Radius: $3$ - X-intercepts: None (no real solutions)