Answer:
[tex]\large\boxed{y=(x-3)^2-3}[/tex]
Step-by-step explanation:
The vertex form of a quadratic equation y = ax² + bx + c:
y = a(x - h)² + k
(h, k) - coordinates of a vertex
We have the equation y = x² - 6x + 6.
Convert to the vertex form:
[tex]y=x^2-2(x)(3)+6\\\\y=\underbrace{x^2-2(x)(3)+3^2}_{(*)}-3^2+6\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\y=(x-3)^2-9+6\\\\y=(x-3)^2-3\to h=3,\ k=-3[/tex]
