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25 November, 18:54

Complete the square to determine the maximum or minimum value of the function defined by the expression. x2 + 8x + 6

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  1. 25 November, 18:59
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    Minimum at (-4, - 10)

    Step-by-step explanation:

    x² + 8x + 6

    The coefficient of x² is positive, so the parabola opens upward, and the vertex is a minimum.

    Subtract the constant from each side

    x² + 8x = - 6

    Square half the coefficient of x

    (8/2) ² = 4² = 16

    Add it to each side of the equation

    x² + 8x + 16 = 10

    Write the left-hand side as the square of a binomial

    (x + 4) ² = 10

    Subtract 10 from each side of the equation

    (x + 4) ² - 10 = 0

    This is the vertex form of the parabola:

    (x - h) ² + k = 0,

    where (h, k) is the vertex.

    h = - 4 and k = - 10, so the vertex is at (-4, - 10).

    The Figure below shows your parabola with a minimum at (-4, - 10).
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