Concept Check Match each equation in Column I with its graph in Column II. I II 47. A. 48. (x - 3)² + (y + 2)² = 25 B. 49. C. 50. D.

Verified step by step guidance

1. Identify the type of equation given in Column I.
2. Recognize that the equation (x - 3)^2 + (y + 2)^2 = 25 is in the form of a circle equation.
3. Understand that the standard form of a circle equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
4. Determine the center of the circle from the equation: (h, k) = (3, -2).
5. Determine the radius of the circle from the equation: r = 5, since 25 is r^2.

Key Concepts

Circle Equation

The equation (x - h)² + (y - k)² = r² represents a circle with center (h, k) and radius r. In this format, h and k are the coordinates of the center, while r is the distance from the center to any point on the circle. Understanding this equation is crucial for identifying the correct graph corresponding to the given equation.

Graphing Techniques

Graphing techniques involve plotting points and understanding the shape of various equations. For circles, one must recognize that the graph will be a closed curve, symmetric about its center. Familiarity with how to translate the algebraic form of an equation into a visual representation is essential for matching equations to their graphs.

Coordinate System

A coordinate system provides a framework for locating points in a plane using ordered pairs (x, y). Understanding how to interpret these coordinates is vital for graphing equations accurately. The position of the center and the radius of a circle can be determined using this system, which aids in visualizing and matching the equations to their respective graphs.