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5 November, 08:48

For what value of h is the expression (x-h) ^2+6 equivalent to the expression x^2-6x+15

For what value of h is the expression (x-h) ^2-6 equivalent to the expression x^2-2x-5

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  1. 5 November, 11:12
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    1. h=3 2. h=1

    Step-by-step explanation:

    You need to make both sides into perfect square trinomials that you factor into the perfect square of a binomial. The left side is almost there to start with.

    ax² + bx + c is the standard equation

    1. (x - h) ² + 6 = x² - 6x + 15 subtract 6 from both sides to get (x - h) ² alone

    - 6 - 6

    (x - h) ² = x² - 6x + 9 factor the right side into a perfect square (b/2)

    here b = - 6 so b/2 = - 3 so (x - 3) ²

    (x - 3) ² = (x - 3) (x - 3) = FOIL (first, outside, inside, last)

    (x) (x) + (-3) (x) + (-3) (x) + (-3) (-3) = x² - 3x - 3x + 9

    = x² - 6x + 9 = (x - 3) ² so

    (x - h) ² = (x - 3) ² so h = 3

    ax² + bx + c is the standard equation

    2. (x - h) ² - 6 = x² - 2x - 5 add 6 to both sides to get (x - h) ² alone

    + 6 + 6

    (x - h) ² = x² - 2x + 1 factor the right side into a perfect square (b/2)

    here b = - 2 so b/2 = - 1 so (x - 1) ²

    (x - 1) ² = (x - 1) (x - 1) = FOIL (first, outside, inside, last)

    (x) (x) + (-1) (x) + (-1) (x) + (-1) (-1) = x² - 1x - 1x + 1

    = x² - 2x + 1 = (x - 1) ² so

    (x - h) ² = (x - 1) ² so h = 1
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