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Math Help - maths homework no going to well

  1. #1
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    Unhappy maths homework no going to well

    express 4x^2 - 12x + 11 in the form a(x+b)^2 +c and hence write down:

    (i) the minimum value of 4x^2 - 12x + 11

    (ii) the maximum value of

    1(over)
    4x^2 - 12x + 11

    thanks

    as an aside

    ^2 is supposed to be squared
    and (ii)is a fraction not very good at this web stuff
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  2. #2
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    4x^2 + 12x + 11

    4(x^2 + 3x) + 11

    4\left[x^2 + 3x + \left(\frac{3}{2}\right)^2 \right] + 11  -  4\left(\frac{3}{2}\right)^2

    4\left[x^2 + 3x + \left(\frac{3}{2}\right)^2 \right] + 11  -  4\left(\frac{9}{4}\right)

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

    ATQ's
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  3. #3
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    express 4x^2 - 12x + 11 in the form a(x+b)^2 +c

    4x^2 - 12x + 11 = 4(x^2 - 3x) + 11
    Comparing x^2 - 3x with the identity
    x^2 + 2px = (x + P)^2 - p^2
    we can match the left-hand sides by putting
    2p = -3; that is p = -3/2
    Putting this value also into the right-hand side, we obtain the completed-square form
    x^2 - 3x = (x - 3/2)^2 - (-3/2)^2 = (x - 3/2)^2 - 9/4
    Hence 4(x^2 - 3x) +11 = 4(x - 3/2)^2 - 9/4) + 11
    = 4(x - 3/2)^2) - (9/4 *4) + 11
    = 4(x - 3/2)^2 - 9 + 11
    So the required form is 4(x 3/2)^2 + 2
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