Characteristics of quadratic functions

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  1. Determining the Characteristics of a Quadratic Function Using Various Methods

    Determine the following characteristics of the quadratic function y=2x2+4x+6y = -2x^2 + 4x + 6 :

    • Opening of the graph

    yy-intercept

    xx-intercept(s)

    • Vertex

    • Axis of symmetry

    • Domain

    • Range

    • Minimum/Maximum value

    1. Using factoring
    2. Using the quadratic formula
    3. Using completing the square
    4. Using the vertex formula
  2. From the graph of the parabola, determine the:
    • vertex
    • axis of symmetry
    • y-intercept
    • x-intercepts
    • domain
    • range
    • minimum/maximum value

    1. characteristics of quadratic functions

    2. Introduction to quadratic functions
  3. Identifying Characteristics of Quadratic function in General Form: y=ax2+bx+cy = ax^2 + bx+c
    y=2x212x+10y = 2{x^2} - 12x + 10 is a quadratic function in general form.

    i) Determine:
    • y-intercept
    • x-intercepts
    • vertex

    ii) Sketch the graph.
    1. Identifying Characteristics of Quadratic Functions in Vertex Form: y=a(xp)2+qy = a(x-p)^2 + q
      y=2(x3)28y = 2{\left( {x - 3} \right)^2} - 8 is a quadratic function in vertex form.

      i) Determine:
      • y-intercept
      • x-intercepts
      • vertex

      ii) Sketch the graph.
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      Topic Notes
      Three properties that are universal to all quadratic functions: 1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior); 2) The domain of a quadratic function is all real numbers; and 3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downward.