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Graphing Quadratic Equations definitions

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  • Quadratic Equation
    An expression in the form y = ax² + bx + c, where a ≠ 0, producing a U-shaped graph.
  • Standard Form
    A way to write quadratics as y = ax² + bx + c, useful for applying the quadratic formula.
  • Vertex Form
    A format y = a(x-h)² + k, making it easy to identify the vertex and graph shifts.
  • Parabola
    The U-shaped curve resulting from graphing any quadratic equation.
  • Vertex
    The highest or lowest point on a parabola, located at (h, k) in vertex form.
  • Axis of Symmetry
    A vertical line passing through the vertex, dividing the parabola into two mirror images.
  • X-Intercept
    A point where the parabola crosses the x-axis, found by setting y to zero.
  • Y-Intercept
    A point where the parabola crosses the y-axis, found by setting x to zero.
  • Quadratic Formula
    A method for finding x-intercepts: x = [-b ± √(b²-4ac)]/(2a).
  • Discriminant
    The value b²-4ac, indicating the number of real x-intercepts a parabola has.
  • Horizontal Shift
    A movement of the parabola left or right, determined by the value of h in vertex form.
  • Vertical Shift
    A movement of the parabola up or down, determined by the value of k in vertex form.
  • Vertical Stretch
    A transformation making the parabola narrower, caused by |a| > 1.
  • Vertical Compression
    A transformation making the parabola wider, caused by 0 < |a| < 1.
  • Opening Direction
    The way the parabola faces, upward if a > 0, downward if a < 0.
  • Domain
    The set of all possible x-values for a parabola, always all real numbers.
  • Range
    The set of possible y-values for a parabola, starting at the vertex and extending up or down.
  • Square Root Property
    A method for solving quadratics by isolating the squared term and taking square roots.
  • Intercept
    A point where the graph crosses an axis, either x or y.
  • Symmetry
    A property where one side of the parabola mirrors the other across the axis of symmetry.
  • Coefficient a
    A value controlling the width and direction of the parabola in both standard and vertex forms.
  • Coefficient b
    A value affecting the position of the axis of symmetry and vertex in standard form.
  • Coefficient c
    A value representing the y-intercept in standard form.
  • Distance from Axis
    The value from the axis of symmetry to each x-intercept, given by the quadratic formula.
  • Real Solution
    A value of x where the quadratic equals zero, corresponding to an x-intercept.
  • Vertical Line
    A line parallel to the y-axis, such as the axis of symmetry.
  • Continuous Curve
    A smooth, unbroken line representing the graph of a quadratic equation.
  • U-Shape
    The characteristic form of a parabola, opening either up or down.