Quadratic Functions: Factored Form Flashcards
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Questions and Answers

Which is the graph of f(x) = -(x + 3)(x + 1)?

  • Graph A
  • Graph B (correct)
  • Graph D
  • Graph C
  • Which function has two x-intercepts, one at (0, 0) and one at (4, 0)?

  • Graph A (correct)
  • Graph D
  • Graph C
  • Graph B
  • The graph of the function f(x) = (x - 4)(x + 1) is shown below. Which statement about the function is true?

  • Statement D (correct)
  • Statement C
  • Statement A
  • Statement B
  • Which is the graph of f(x) = (x - 1)(x + 4)?

    <p>Graph D</p> Signup and view all the answers

    What is the axis of symmetry of the function f(x) = -(x + 9)(x - 21)? The axis of symmetry is x =

    <p>6</p> Signup and view all the answers

    The function f(x) = −(x + 5)(x + 1) is shown. What is the range of the function?

    <p>Range A</p> Signup and view all the answers

    Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x - 3)?

    <p>Point D</p> Signup and view all the answers

    The function f(x) = (x − 4)(x − 2) is shown. What is the range of the function?

    <p>Range D</p> Signup and view all the answers

    The graph of the function f(x) = (x + 2)(x + 6) is shown below. Which statement about the function is true?

    <p>Statement B</p> Signup and view all the answers

    What is the y-intercept of the quadratic function f(x) = (x - 8)(x + 3)?

    <p>Option C</p> Signup and view all the answers

    What is the y-intercept of the quadratic function f(x) = (x - 6)(x - 2)?

    <p>B</p> Signup and view all the answers

    What is the midpoint of the x-intercepts of f(x) = (x - 2)(x - 4)?

    <p>D</p> Signup and view all the answers

    Which function has only one x-intercept at (−6, 0)?

    <p>Graph D</p> Signup and view all the answers

    The graph of the function f(x) = (x − 3)(x + 1) is shown. Which describes all of the values for which the graph is positive and decreasing?

    <p>Values A</p> Signup and view all the answers

    Study Notes

    Quadratic Functions: Factored Form

    • The function f(x) = -(x + 3)(x + 1) has a graph that opens downwards, indicating a maximum point.
    • The function with x-intercepts at (0, 0) and (4, 0) represents a quadratic that crosses the x-axis twice.
    • The function f(x) = (x - 4)(x + 1) shows characteristics such as x-intercepts and can be analyzed for key features.
    • The graph of f(x) = (x - 1)(x + 4) features distinct x-intercepts that can be identified graphically.
    • The axis of symmetry for f(x) = -(x + 9)(x - 21) is located at x = 6, dividing the graph into two symmetrical halves.
    • The range of the function f(x) = −(x + 5)(x + 1) is determined by the maximum value since it opens downwards.
    • For the function f(x) = (x + 6)(x - 3), identifying x-intercepts is crucial for understanding its roots.
    • The range of f(x) = (x − 4)(x − 2) can be deduced from its vertex, as it opens upwards.
    • The function f(x) = (x + 2)(x + 6) can be analyzed for true statements regarding its behavior and key attributes.
    • The y-intercept of f(x) = (x - 8)(x + 3) can be calculated by evaluating the function at x = 0.
    • The y-intercept for f(x) = (x - 6)(x - 2) is found by substituting 0 into the function.
    • The midpoint of the x-intercepts for f(x) = (x - 2)(x - 4) provides insights into the vertex's horizontal position.
    • A quadratic function that has only one x-intercept, such as (−6, 0), is termed a perfect square trinomial.
    • The function f(x) = (x − 3)(x + 1) is characterized by specific intervals where it is positive and decreasing.

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    Test your understanding of quadratic functions in factored form with these flashcards. Each card presents a function and challenges you to identify characteristics or graphs related to it. Perfect for students looking to reinforce their algebra skills!

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