Answer
Vertex: $(3, 2)$
Opens upward
x-intercepts: none
y-intercept: 11
Work Step by Step
$f(x)=x^2-6x+11$
$y=x^2-6x+11$
$y-2=x^2-6x+11-2$
$y-2=x^2-6x+9$
$y-2=(x-3)^2$
$y-2+2=(x-3)^2+2$
$y=(x-3)^2+2$
Vertex: $(3, 2)$
Opens upward
Since the vertex is above the x-axis and the graph opens upward, the graph has no x-intercepts.
$x=0$
$f(x)=x^2-6x+11$
$f(0)=0^2-6*0+11$
$f(0)=0-0+11$
$f(0)=11$
x-intercepts: none
y-intercept: 11
