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Quadratic Functions definitions

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  • Quadratic Function
    A polynomial of degree 2 with a graph that forms a parabola, typically written as f(x) = ax^2 + bx + c with a ≠ 0.
  • Standard Form
    An expression of a quadratic as f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a ≠ 0.
  • Vertex Form
    A representation of a quadratic as f(x) = a(x-h)^2 + k, highlighting the vertex (h, k) and transformations.
  • Parabola
    The U-shaped curve formed by the graph of any quadratic function, opening upward or downward.
  • Vertex
    The point on a parabola representing its maximum or minimum value, located at (h, k) in vertex form.
  • Axis of Symmetry
    A vertical line passing through the vertex, dividing the parabola into two mirror-image halves, given by x = h.
  • X-Intercept
    A point where the parabola crosses the x-axis, found by solving f(x) = 0; can be one or two points.
  • Y-Intercept
    The point where the parabola crosses the y-axis, found by evaluating f(0).
  • Domain
    The set of all possible input values for a quadratic function, always all real numbers.
  • Range
    The set of possible output values for a quadratic, determined by the vertex and the direction the parabola opens.
  • Minimum
    The lowest point on a parabola, occurring at the vertex when the parabola opens upward.
  • Maximum
    The highest point on a parabola, occurring at the vertex when the parabola opens downward.
  • Vertical Stretch
    A transformation making the parabola narrower, caused by |a| > 1 in the quadratic's equation.
  • Vertical Compression
    A transformation making the parabola wider, caused by 0 < |a| < 1 in the quadratic's equation.
  • Completing the Square
    A method for rewriting a quadratic in standard form into vertex form by creating a perfect square trinomial.