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To find the center and radius of the circle given by the equation:

\[
(x + 4)^2 + (y - 1)^2 = 4
\]

we need to identify it in the standard form of a circle's equation:

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

### Step-by-Step Solution

1. **Identify the Center \((h, k)\):**
   - In the equation \((x + 4)^2 + (y - 1)^2 = 4\), we have \((x - (-4))^2\) and \((y - 1)^2\).
   - This tells us the center \((h, k)\) is at \((-4, 1)\).

2. **Find the Radius \(r\):**
   - The right side of the equation is 4, which is \(r^2\).
   - Solving for \(r\), we get \(r = \sqrt{4} = 2\).

### Answer

- **Center:** \((-4, 1)\)
- **Radius:** \(2\)

Now, to graph the circle:
1. Plot the center at \((-4, 1)\).
2. Draw a circle with a radius of 2 units from the center, ensuring it spans 2 units in all directions around the center.

Would you like further explanation on graphing or any other details?

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### Follow-up Questions

1. How can you rewrite an equation to identify the center and radius of a circle?
2. What does changing the values of \(h\) and \(k\) do to the position of the circle?
3. How is the radius calculated when given an equation of a circle?
4. What is the significance of the radius in the graph of a circle?
5. How would you graph a circle with a center at the origin?

### Tip:
When identifying the radius in a circle equation, remember that \(r\) is the square root of the constant on the right side.

The equation of a circle is given below. Identify the center and radius, then graph the circle. (x + 4)^2 + (y - 1)^2 = 4

Learn how to identify the center and radius of a circle given the equation (x + 4)^2 + (y - 1)^2 = 4. This lesson covers the standard form of a circle's equation and graphing tips. Suitable for Grades 9-10.

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