completing the square
posted by rebekah on .
1. f(x)= x^24
2. f(x)= x^2+6x+9
3. f(x) = 3x^28x+2

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( (x4/3)^2  19/9 ) + 2 , write the first 3 terms in the bracket as a perfect square
= 3(x4/3)^2  16/3 + 2 , distribute the 3 over the inside of the bracket
= 3(x4/3)^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