https://file.aiquickdraw.com/mathbot/file/1726102837547th3wh9xw.jpg

The equation provided in the image \((x+3)^2 + (y-2)^2 = 16\) describes a circle in the coordinate plane. Here's how you can graph it:

1. **Identify the center and radius of the circle:**
   - The center of the circle is found by setting each squared term to zero and solving for \(x\) and \(y\). This gives us a center at \((-3, 2)\).
   - The radius is the square root of the constant term on the right side of the equation. Here, the radius is \(\sqrt{16} = 4\).

2. **Graphing the circle:**
   - Start by plotting the center at point \((-3, 2)\) on the coordinate grid.
   - From the center, move out 4 units in all directions (up, down, left, right) to mark points on the circle.
   - Connect these points in a smooth, round shape to complete the circle.

Here's a step-by-step visualization:
- **Center**: Plot the point at \((-3, 2)\).
- **Radius Points**: Plot points at \((-3 + 4, 2) = (1, 2)\), \((-3 - 4, 2) = (-7, 2)\), \((-3, 2 + 4) = (-3, 6)\), and \((-3, 2 - 4) = (-3, -2)\).
- **Drawing the circle**: Connect these points smoothly to form a circle.

Would you like a detailed guide on drawing the circle, or do you have any other questions?

Relative Questions:
1. How would the graph change if the equation was \((x+3)^2 + (y-2)^2 = 9\)?
2. What does the equation \((x-4)^2 + (y+5)^2 = 25\) represent on a graph?
3. How can you determine if a point lies inside, on, or outside this circle?
4. Can you convert this circle equation to parametric form?
5. How would changing the sign of the constant inside the squared terms affect the circle's position?

Tip: When graphing a circle by hand, using a compass set to the radius distance helps ensure accuracy and symmetry.

Graph the circle: (x + 3)^2 + (y - 2)^2 = 16

Learn how to graph the circle with the equation (x + 3)^2 + (y - 2)^2 = 16. This problem involves understanding the center-radius form of a circle equation, identifying the center at (-3, 2) and the radius as 4. Suitable for students in Grades 9-10.

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