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Quadratic Functions quiz

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  • What is the standard form of a quadratic function?
    The standard form is f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a ≠ 0.
  • What shape does the graph of a quadratic function always take?
    The graph is always a parabola, which can open upwards or downwards.
  • How do you determine if the vertex of a parabola is a minimum or maximum?
    If the parabola opens upward (a > 0), the vertex is a minimum; if it opens downward (a < 0), the vertex is a maximum.
  • What is the axis of symmetry for a parabola in vertex form?
    The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.
  • How many x-intercepts can a quadratic function have?
    A quadratic function can have one or two x-intercepts, but never more or less.
  • What is the domain of any quadratic function?
    The domain is all real numbers, written as (−∞, ∞).
  • How does the value of 'a' in vertex form affect the parabola's width?
    If |a| > 1, the parabola is vertically stretched (narrower); if |a| < 1, it is vertically compressed (wider).
  • What does the 'h' value in vertex form indicate?
    The 'h' value indicates a horizontal shift of the parabola by h units.
  • How do you find the y-intercept of a quadratic function?
    Plug x = 0 into the function and solve for f(0).
  • What is the vertex of a quadratic function in vertex form f(x) = a(x-h)^2 + k?
    The vertex is the point (h, k).
  • How do you find the x-intercepts of a quadratic function in vertex form?
    Set f(x) = 0 and solve for x, often using the square root property.
  • What is the process called for converting standard form to vertex form?
    The process is called completing the square.
  • What is the range of a quadratic function with a minimum at y = k?
    The range is [k, ∞) if the parabola opens upward.
  • How do you determine the intervals where a quadratic function is increasing or decreasing?
    The vertex divides the intervals; the function increases on one side of the vertex and decreases on the other.
  • What steps are involved in completing the square for f(x) = ax^2 + bx + c?
    Factor out a from the x terms, add and subtract (b/2a)^2 inside the parentheses, move the subtracted term outside, and rewrite in vertex form.