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7 June, 21:13

Using the completing-the-square method, rewrite f (x) = x^2-6x+2 in vertex form.

- f (x) = (x-3) ^2

- f (x) = (x-3) ^2 + 2

- f (x) = (x-3) ^2 - 7

- f (x) = (x-3) ^2 + 9

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  1. 7 June, 21:33
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    The vertex form of f (x) is f (x) = (x - 3) ² - 7 ⇒ 3rd answer

    Step-by-step explanation:

    To make a bracket of power two from a quadratic expression do that

    Take the term of x and divide its coefficient by 2 Square the quotient Add and subtract this square to the quadratic expression Simplify it and write it in the form (x - h) ² + k

    ∵ f (x) = x² - 6x + 2

    ∵ x² = (x) (x)

    ∴ The first term in the bracket of power 2 is x

    - Divide - 6x by 2

    ∵ - 6x : 2 = - 3x

    ∴ The second term in the bracket of power 2 is - 3

    - Square (-3)

    ∵ (-3) ² = 9

    - Add and subtract 9 to f (x)

    ∴ f (x) = x² - 6x + 9 - 9 + 2

    ∴ f (x) = (x² - 6x + 9) - 9 + 2

    - Write (x² - 6x + 9) in the form (x - 3) ²

    ∴ f (x) = (x - 3) ² - 9 + 2

    - Add the like terms in the right hand side

    ∴ f (x) = (x - 3) ² - 7

    ∴ The vertex form of f (x) is f (x) = (x - 3) ² - 7
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