Answer: \(9\left(x-\dfrac23\right)^2+1\); minimum point \(\left(\dfrac23,1\right)\).

(a) Complete the square:

\(9x^2-12x+5 =9\left(x^2-\frac43x\right)+5.\)

Now

\(x^2-\frac43x =\left(x-\frac23\right)^2-\frac49.\)

Therefore

\(9x^2-12x+5 =9\left[\left(x-\frac23\right)^2-\frac49\right]+5.\)

So

\(9x^2-12x+5 =9\left(x-\frac23\right)^2-4+5.\)

Hence

\(9x^2-12x+5=9\left(x-\frac23\right)^2+1.\)

(b) From the completed-square form, the minimum point is

\(\left(\frac23,1\right).\)