completing the square

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1. f(x)= x^2-4
2. f(x)= x^2+6x+9
3. f(x) = 3x^2-8x+2

  • completing the square -

    I will do the last one, the hardest of the three

    3. f(x) = 3x^2 - 8x + 2
    = 3(x^2 - (8/3)x) + 2 , factor out the coefficient of the x^2 term from the terms containing x

    = 3( x^2 - (8/3)x + 16/9 - 16/9) + 2 , take 1/2 of the coefficient of the x term, square it, then add and subtract it
    = 3( (x-4/3)^2 - 19/9 ) + 2 , write the first 3 terms in the bracket as a perfect square
    = 3(x-4/3)^2 - 16/3 + 2 , distribute the 3 over the inside of the bracket
    = 3(x-4/3)^2 - 16/3 + 6/3 , using a common denominator ....

    = 3(x - 4/3)^2 -10/3 , add up the constants

    f(x) = 3(x - 4/3)^2 - 10/3

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