First, consider that a quadratic equation in vertex form is given by:
[tex]y=a(x-h)^2+k[/tex]
where a is the leading coefficient and (h,k) is the vertex of the curve.
You have the following equation:
[tex]y=x^2-6x+12[/tex]
In this case, the leading coefficient is a = 1.
The vertex is determined as follow:
Use the following formula to find h:
[tex]h=-\frac{b}{2a}=-\frac{-6}{2(1)}=3[/tex]
where we have used b = -6.
Now, to find k use:
[tex]f(h)=(3)^2-6(3)+12=9-18+12=3[/tex]
Then, h = 3 and k = 3.
By replacing the values of a, h and k, you obtain:
[tex]y=(x-3)^2+3[/tex]
The previous result is the given equation in vertex form.
