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2 September, 04:52

What are the vertex, axis of symmetry, maximum or minimum value, and range of y = 3x^2 + 6x - 1?

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  1. 2 September, 05:21
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    The vertex is when x=-b/2a, which is also the line of symmetry.

    in this case, b=6, a=3, so x=-6/6=-1

    when x=-1. y=3-6-1=-4

    another way to do it is to write the equation into vertex form by making a square:

    3x²+6x-1

    3 (x²+2x-1/3)

    3 (x²+2x+1-1-1/3))

    3 (x²+2x+1-4/3))

    notice the bold part makes a square:

    3 (x+1) ²-4

    Either way,

    the vertex is (-1, - 4)

    the axis of symmetry is x=-1

    the coefficient of x² is 3, a positive number, so this parabola opens upward. the function has a minimum value of y=-4

    the range is all real number larger than - 4
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