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Completing square? watch

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    The question is:
    The function f is given by f: x-> 7-12x-4x^2, x E R
    a) Find the values of the positive constants A, B and C for which:
    A-(Bx+C)^2=7-12x-4x^2

    I did as follows:
    LHS:
    7-12x-4x^2
    =-4[x^2+12x-7/4]
    =-4[x^2+12x+36-36+7/4]
    =-4[(x+36)^2-151/4]
    =-4(x+6)^2+151
    =151-4(x+6)^2

    This isn't in the form A-(Bx+C)^2 (because of the -4 before (x+6) bracket) and the answers are wrong. What did I do wrong? Am I supposed to complete square?
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    Your mistake is in the 2nd line- it should be:

    -4[x^2+3x-(7/4)]
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    In regard to trying to get the answer in that form, you have to be able to spot a little thing.
    Firstly, by completing the square, you should get:

    23 - 4(x+2)^2

    Notice that 4 = 2^2

    = 23 - (2^2)(x+2)^2

    Now, you can group the '2' and the (x+2), and square the whole thing

    = 23 - [2(x+2)]^2

    = 23 - (2x+4)^2
    • Thread Starter
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    Thanks for your quick help. I got -4x^2-12x+7 when I completed square, which gave A=16, B=2, C=3. That's a bit clever to notice the 2^2 part!
 
 
 
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