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Graphing Circles definitions

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  • Standard Form
    Equation format revealing center and radius, enabling direct graphing by identifying key circle features.
  • General Form
    Expanded equation requiring algebraic manipulation to expose geometric properties for graphing.
  • Radius
    Constant distance from the center to any point on the circle, crucial for plotting and defining size.
  • Center
    Ordered pair marking the exact location around which all points of the circle are equidistant.
  • Origin
    Point (0,0) on the coordinate plane, often used as a special case for circle centers.
  • Completing the Square
    Algebraic process transforming polynomials into perfect square trinomials to reveal circle parameters.
  • Perfect Square Trinomial
    Polynomial form resulting from completing the square, essential for converting equations.
  • Ordered Pair
    Two-number notation specifying a point’s location, used for identifying the center.
  • Constant
    Fixed value in an equation, often moved to isolate variables during conversion steps.
  • Factor
    Expression rewritten as a product, used to simplify and clarify circle equations.
  • Coordinate Plane
    Grid system for plotting points, essential for visualizing circles and their features.
  • Polynomial
    Algebraic expression with multiple terms, forming the basis of circle equations.
  • Equality
    State maintained during algebraic manipulation, ensuring both sides of an equation remain balanced.
  • Square Root
    Operation used to determine the radius from its squared value in the equation.
  • Smooth Curve
    Continuous line connecting plotted points, visually representing the circle on a graph.