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26 August, 12:46

Compete the square to determine minum or maxuim value of function define by - x2+10x+5

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  1. 26 August, 13:02
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    maximum value y = 30

    Step-by-step explanation:

    Given

    - x² + 10x + 5

    To complete the square the coefficient of the x² term must be 1

    factor out - 1

    = - (x² - 10x) + 5

    To complete the square

    add/subtract (half the coefficient of the x - term) ² to x² - 10x

    = - (x² + 2 ( - 5) x + 25 - 25) + 5

    = - (x - 5) ² + 25 + 5

    = - (x - 5) ² + 30 ← in vertex form

    y = a (x - h) ² + k

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

    Hence vertex = (5, 30)

    The max / min occurs at the vertex

    Since a < 0 then vertex is a maximum

    Hence maximum value is y = 30
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