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Math Help - Complete the Square

  1. #1
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    Complete the Square

    Complete the square of the given function.

    f(x) = x^2 - 6x

    HINT GIVEN:

    If f(x) = x^2 - 2x, then f(x) = (x^2 - 2x + 1) - 1 = (x - 1)^2 - 1.

    I am looking for steps.

    Sample:

    Step 1: do this

    Step 2: do that, etc.
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  2. #2
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    Re:

    RE:


    -qbkr21
    Attached Thumbnails Attached Thumbnails Complete the Square-34.jpg  
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  3. #3
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    Tell me...

    Where did the fraction (-6/2) come from?
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  4. #4
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    If you have an expression, say
    x^2 + 3x
    that you need to complete the square of, consider the following:
    x^2 + 2ax + a^2 = (x + a)^2

    So we wish to add a number to our expression to put it in the above form.

    So equate the coefficients of the linear terms:
    3 = 2a

    Thus
    a = \frac{3}{2}

    According to the prescription, then, we need to add an a^2 to our x^2 + 3x to make it a perfect square. But what we add on one side, we must also subtract (so we're adding a net of zero to that side), thus:
    x^2 + 3x = x^2 + 3x + \left ( \frac{3}{2} \right ) ^2 - \left ( \frac{3}{2} \right ) ^2

    = \left ( x + \frac{3}{2} \right ) ^2 - \left ( \frac{3}{2} \right ) ^2

    -Dan
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  5. #5
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    Quote Originally Posted by blueridge View Post
    Where did the fraction (-6/2) come from?
    x^2 - 6x

    When you complete the square you add (1/2) of the middle term squared.

    So \frac{6}{2} = 3 and squared is 9.
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