Question

Which graph is correct?

Answer 1

Answer:

D

Step-by-step explanation:

The equation for a circle is

(x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

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

Rewritng

(x- -2)^2 + (y-0)^2 = 2^2

The center is at ( -2,0) and the radius is 2

C and D are the only circles with a center at (-2,0)

B,D are the only circles with radius 2

Answer 2

Let's first take a look at our x here. --- (x + 2)^2

Because we are adding a two to our x, this means that we are shifting our graph 2 to the left. Remember that with functions, it's always the opposite!

There is nothing attached to the y, so we are not moving our function up or down.

And then the radius of our circle. Remember that the equation requires us to square this value (... = r^2), so we need to take the square root of 4. The square root of 4 is 2.

With this information, let's now look at our options.

Option A - INCORRECT, the radius is too large

Option B - INCORRECT, this was shifted 2 units to the right

Option C - INCORRECT, the radius is too large

Option D - CORRECT, the radius is 2 and the circle was shifted 2 units to the left

Hope this helps!! :)