quadratic

3x^2 + 4x + 1     divide by 3

x^2 + 4/3 x + 1/3     complete the square

(x+ 4/6)^2   -16/36 +1/3 =

 

(x + 4/6)^2  - 1/9        now put the '3' back in

3 (x+4/6)^2 -1/3         now you can see  a   h   and k

We complete the square.

 

\(3x^2+4x+1\\ =3(x^2+\frac{4}{3}x+\frac{1}{3})\\ =3(x+\frac{2}{3})^2-\frac{1}{3}\)

 

So a=3, h=2/3, and k=-1/3.