In Exercises 95-102, a) use the method of completing the...

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Key Concepts

Graphing Equations – Circles

Graphing a circle involves plotting its center on the coordinate plane and drawing a circle with a radius equal to the square root of the constant on the right side of the standard form equation. This process translates the algebraic equation into a visual representation, assisting in the analysis of the circle's geometric properties and its relation to other figures on the graph.

Completing the Square

Completing the square is an algebraic method used to transform a quadratic expression into a perfect square trinomial plus or minus a constant. This technique is essential in rewriting quadratic equations in a form that reveals important properties about the graph, such as the center and radius in the context of circles, or the vertex in the context of parabolas.

Standard Form of a Circle

The standard form of a circle’s equation is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r is the radius. Converting a general second-degree equation into this form through completing the square makes it easier to understand the geometric attributes of the circle, including its location and size.

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