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Graphing Quadratic Equations definitions

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  • Quadratic Equation
    An equation in the form y = ax² + bx + c, where a ≠ 0, producing a U-shaped graph.
  • Standard Form
    The arrangement y = ax² + bx + c, used for identifying key graph features.
  • Parabola
    A smooth, U-shaped curve representing the graph of a quadratic equation.
  • Vertex
    The highest or lowest point on a parabola, indicating its maximum or minimum value.
  • Axis of Symmetry
    A vertical line passing through the vertex, dividing the parabola into two mirror halves.
  • X-Intercept
    A point where the graph crosses the x-axis, found by solving the equation for y = 0.
  • Y-Intercept
    A point where the graph crosses the y-axis, found by setting x = 0 in the equation.
  • Quadratic Formula
    A method for finding x-intercepts, given by x = [-b ± √(b²-4ac)]/(2a).
  • Discriminant
    The expression b²-4ac, indicating the number of real x-intercepts a parabola has.
  • Ordered Pair
    A set (x, y) representing a specific point on the graph.
  • Coefficient
    A numerical factor (like a, b, or c) in the quadratic equation affecting the graph's shape.
  • Opening Direction
    The way a parabola faces, upward if a > 0, downward if a < 0.
  • Maximum Point
    The vertex when the parabola opens downward, representing the highest value.
  • Minimum Point
    The vertex when the parabola opens upward, representing the lowest value.
  • Symmetry
    A property where one side of the parabola mirrors the other across the axis of symmetry.
  • Distance to X-Intercept
    The value from the axis of symmetry to each x-intercept, given by the square root part of the quadratic formula.
  • Continuous Curve
    A graph with no breaks, representing the smooth shape of a parabola.
  • Solution
    A value of x that makes the quadratic equation true when y = 0, corresponding to x-intercepts.
  • High Point
    The vertex when the parabola opens downward, also called the maximum.
  • Low Point
    The vertex when the parabola opens upward, also called the minimum.
  • Vertex Formula
    The calculation x = -b/(2a), used to find the x-value of the vertex and axis of symmetry.