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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 is a curved, symmetric shape.
  • How do you determine if the vertex of a parabola is a maximum or minimum?
    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 vertex form of a quadratic function?
    The vertex form is f(x) = a(x - h)^2 + k, where (h, k) is the vertex.
  • How do you find the axis of symmetry for a quadratic in vertex form?
    The axis of symmetry is the vertical line x = h, passing through the vertex.
  • What is the domain of any quadratic function?
    The domain is all real numbers, written as (−∞, ∞).
  • How do you find the range of a quadratic function with a minimum at y = k?
    The range is [k, ∞) if the parabola opens upward.
  • How does the value of 'a' in vertex form affect the graph's width?
    If |a| > 1, the parabola is vertically stretched (narrower); if 0 < |a| < 1, it is vertically compressed (wider).
  • What does the 'h' value in vertex form represent?
    The 'h' value represents a horizontal shift of the parabola by h units.
  • How do you find the x-intercepts of a quadratic in vertex form?
    Set f(x) = 0 and solve for x, often using the square root property.
  • How do you find the y-intercept of a quadratic function?
    Substitute x = 0 into the function and solve for f(0).
  • What is the process called for converting a quadratic from standard to vertex form?
    The process is called completing the square.
  • What is the formula for the axis of symmetry in standard form?
    The axis of symmetry is x = -b/(2a).
  • How do you determine the intervals where a parabola is increasing or decreasing?
    The graph increases to the vertex and decreases after the vertex (or vice versa), with the vertex dividing the intervals.
  • What are the steps to graph a quadratic in vertex form?
    Find the vertex (h, k), determine if it is a min or max, plot the axis of symmetry, find x- and y-intercepts, and sketch the parabola.