Well, first we need to know the equation of a circle. It is (x−xv)2+(y−yv)2=r2. xv is the value of x at the vertex, yv is the value of y at the vertex, and r is the radius.
Now we should start filling in the equation with what we know. xv is −2 and yv is 1. We don't know the radius, but I bet we can find it using the distance formula. To use the distance formula we plot the two points we know ((−2,1) and (1,0)) and draw a right triangle from them. The y components are one leg and the x components give us another leg. Then we solve for the hypotenuse using pythagorean's theorem.
So, if the points we have are (−2,1) and (1,0), then the y leg is 1−0, which is 1. For the x leg, we subtract -2 from 1 to give us 3. So, the two legs are 1 and 3. Now we solve for the hypotenuse (a2+b2=c2). 12+32=c2 or 9+1=c2. That means that 10=c2 and that c=√10. Now we have the hypotenuse, which is also the radius.
Once we fill in the formula we arrive at (x−(−2))2+(y−1)2=√102. To confirm we got it right, let's graph it:
graph{(x+2)^2+(y-1)^2=10}
The vertex is at (−2,1) and the circle hits the point (1,0). We are correct!
