If we express $3x^2 + x - 4$ in the form $a(x - h)^2 + k$, then what is $k$?
3x^2 + x - 4 factor out the 3
3 [x^2 + (1/3)x - (4/3) ]
Take (1/2) of (1/3) = 1/6.......square this = 1/36......add it and subtract it
3 [ x^2 + (1/3)x + 1/36 - (4/3) - 1/36 ] factor the first 3 terms
3 [ ( x + 1/6)^2 - 1/36 - 48/36 ]
3 [ (x + 1/6)^2 - 49/36 ]
3(x + 1/6)^2 - 49/12
So k = -49/12
Thank you so much I was struggling with completing the square now I get it