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13 August, 08:04

Complete the square to rewrite y = x2 - 6x + 3 in vertex form. Then state

whether the vertex is a maximum or a minimum and give its coordinates.

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Answers (1)
  1. 13 August, 09:35
    0
    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

    Given

    y = x² - 6x + 3

    To complete the square

    add/subtract (half the coefficient of the x - term) ² to x² - 6x

    y = x² + 2 ( - 3) x + 9 - 9 + 3

    = (x - 3) ² - 6 ← in vertex form

    • If a > 0 then vertex is a minimum

    • If a < 0 then vertex is a maximum

    Here a = 1 > 0, thus

    (3, - 6) is a minimum
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