Question 805484
{{{9x^2-12x+4=-3}}}

Factor the 9 from {{{9x^2-12x}}}:
{{{9(x^2-(12/9)x)}}}
{{{9(x^2-(4/3)x)}}}


Form the missing square term, {{{((4/3)/2)^2=4/9}}};
You must add {{{(4/9)*9}}} to both sides of the equation, being careful to account for what is inside and what is outside the factored grouping from your previous factoring step.


Watch this step carefully:
{{{9(x^2-(4/3)x+4/9)+4=-3+(4/9)*9}}}


Start simplifying.
{{{9(x-2/3)^2+4=-3+4}}}
{{{9(x-2/3)^2=-3+4-4}}}
{{{9(x-2/3)^2=-3}}}


If you want to solve for x, you can from that.  "Vertex" form suggests you have a function but you did not show a given function, but a quadratic equation.  Maybe {{{highlight(f(x)=9(x-2/3)^2+3)}}}  ?
The vertex is (2/3, 3).