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Math Help - Graph of the Function

  1. #1
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    Graph of the Function

    If the roots of
    ax^2 + bx + c = 0 are real, rational, and equal, what is true about the graph of the function
    y = ax^2 + bx + c?

    (1) It intersects the
    x-axis in two distinct points.
    (2) It lies entirely below the
    x-axis.
    (3) It lies entirely above the
    x-axis.

    (4) It is tangent to the
    x-axis.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    If the roots of

    ax^2 + bx + c = 0 are real, rational, and equal, what is true about the graph of the function

    y = ax^2 + bx + c?

    (1) It intersects the x-axis in two distinct points.
    (2) It lies entirely below the x-axis.
    (3) It lies entirely above the x-axis.
    (4) It is tangent to the x-axis.
    The answer is (4) It is tangent to the x-axis.

    If the roots are equal, then it is called a 'double root', thus touching the x-axis at only one point, the point of tangency to the x-axis (also the vertex of the parabola). A double root also refers to a zero of a polynomial function with multiplicity 2.

    Example: y=x^2+4x+4

    x^2+4x+4=0

    (x+2)(x+2)=0

    x=2 \ \ or \ \ x=2

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  3. #3
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    tell me.........

    Quote Originally Posted by masters View Post
    The answer is (4) It is tangent to the x-axis.

    If the roots are equal, then it is called a 'double root', thus touching the x-axis at only one point, the point of tangency to the x-axis (also the vertex of the parabola). A double root also refers to a zero of a polynomial function with multiplicity 2.

    Example: y=x^2+4x+4

    x^2+4x+4=0

    (x+2)(x+2)=0

    x=2 \ \ or \ \ x=2
    Tell me, where do you find the answers? How do you know so much about math? Do you search online for the answers or your math books?
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