question determine the equation of the circle graphed below.

Explanation:

Step1: Identify center coordinates

By observing the graph, the center of the circle $(h,k)$ is at $(4,2)$.

Step2: Determine the radius

Counting the grid - squares, the radius $r = 2$.

Step3: Use the standard circle equation

The standard equation of a circle is $(x - h)^2+(y - k)^2=r^2$. Substitute $h = 4$, $k = 2$, and $r = 2$ into the equation: $(x - 4)^2+(y - 2)^2=4$.

Answer:

$(x - 4)^2+(y - 2)^2=4$