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complete the square to rewrite y=x^2+8x+7 in vertex form and then identify the minimum y value of the function

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  1. 6 May, 16:32
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    see explanation

    Step-by-step explanation:

    The equation of a parabola in vertex form is

    y = a (x - h) ² + k

    where (h, k) are the coordinates of the vertex and a is a multiplier

    To obtain this form use the method of completing the square

    add / subtract (half the coefficient of the x - term) ² to x² + 8x

    y = x² + 2 (4) x + 4² - 4² + 7 ← complete the square

    = (x + 4) ² - 16 + 7

    = (x + 4) ² - 9 ← in vertex form

    with vertex = ( - 4, - 9)

    The minimum value is the y value of the vertex

    Minimum value = - 9 when x = - 4
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