I don't understand this question!
All it says is:
Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit.

x^2 + 2x + y^2 + 4y = 20

x^2 + 2x + y^2 + 4y = 20

Let's break it into 2 parts.

x^2 + 2x and y^2 + 4y

What do you need to add to x^2 + 2x to make it a square of a binomial? It's the square of half the coefficient of x. In other words, (2/2) ^ 2, which is 1. So, you add 1.

x^2 + 2x + 1

Do the same for y^2 + 4y. (4/2) ^ 2 = 2^2 = 4. So, we add 4.

y^2 + 4y + 4.

But, we added a 1 and a 4. These can't just come out of nowhere. So, we need to add a 1 and a 4 to the other side of the equation as well. Right now, we have:

x^2 + 2x + 1 + y^2 + 4y + 4 = 20 + 1 + 4

What is x^2 +2x + 1 the square of? x + 1. How about y^2 + 4y + 4? x + 2. If we factor each of these and simplify the sum on the right side of the equation, we'll have rewritten the equation fully.

(x + 1)^2 + (y + 2)^2 = 25

Now, we need the center. Take the negative of the constant being added to each variable, and you'l have it. Here, we have 1 and 2. That means the center of the circle is (-1, -2).

How about the radius? It's the square root of that sum on the right side of the equation. The square root of 25 is 5, which is the radius.

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis

a

step-by-step explanation: