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Quadratic Functions definitions

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  • Quadratic Function
    A polynomial of degree 2, typically written as f(x) = ax² + bx + c, whose graph forms a parabola.
  • Parabola
    A symmetric, curved graph representing all quadratic functions, opening upward or downward.
  • Standard Form
    An expression of a quadratic as f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.
  • Vertex
    The point on a parabola representing either its maximum or minimum, given as an ordered pair.
  • Axis of Symmetry
    A vertical line passing through the vertex, dividing the parabola into two mirror-image halves.
  • X-Intercept
    A point where the parabola crosses the x-axis, found by solving f(x) = 0.
  • Y-Intercept
    A point where the parabola crosses the y-axis, found by evaluating f(0).
  • Vertex Form
    A quadratic written as f(x) = a(x-h)² + k, making transformations and the vertex easy to identify.
  • Domain
    The set of all possible x-values for a quadratic, always all real numbers.
  • Range
    The set of possible y-values for a quadratic, determined by the vertex and the direction the parabola opens.
  • Vertical Stretch
    A transformation making the parabola narrower, occurring when |a| > 1 in the quadratic equation.
  • Vertical Compression
    A transformation making the parabola wider, occurring when 0 < |a| < 1 in the quadratic equation.
  • 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.
  • Completing the Square
    A method for rewriting a quadratic from standard to vertex form by creating a perfect square trinomial.