Identify the center and radius of each. Photo attached.

Center ~ ( -4, 3 ), Radius ~ 2; Option A

Step-by-step explanation:

~ We know that the standard circle equation ( x - a )^2 + ( y - b )^2 = r^2  provided r ⇒ radius of the circle, centered at ( a, b ) ~

1. If we are given the circle formula ( x + 4 )^2 + ( y - 3 )^2 = 4, it would be that the center points ( a, b ) would be the inverse of 4 and -3, provided the formula is -a and -b: center ( -4, 3 )

2. Now the radius in the formula ( x - a )^2 + ( y - b )^2 = r^2, is noted by r such that in ( x + 4 )^2 + ( y - 3 )^2 = 4, r^2 is 4 ⇒ r = √4 = 2

3. We now know that the center of this circle is ( -4, 3 ) with a radius of 2, and the only graph that represents that function is the first graph ~

Center ~ ( -4, 3 ), Radius ~ 2

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.