The diameter of a circle has endpoints whose coordinates are R(-2, 2) and S(4, 2).
Find the center of the circle.

(1, 2)

Step-by-step explanation:

The diameter of a circle is a straight line beginning and ending at opposite ends of a circle.

The center of a circle will always fall on the midpoint of the diameter.

The line given is horizontal and six units long.

As such, the midpoint is three units to the right of (-2, 2) and three units to the left of (4, 2). The correct midpoint is (1, 2).

This is the center of the circle.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1