Answer
Vertex: $(2,3)$
Opens upward
x-intercept: none
y-intercept: 11
Work Step by Step
$f(x)=2x^2-8x+11$
Vertex: $x=-b/2a$
$x=-b/2a$
$x=-(-8)/2*2$
$x=8/4$
$x=2$
$f(x)=2x^2-8x+11$
$f(2)=2*2^2-8*2+11$
$f(2)=2*4-16+11$
$f(2)=8-5$
$f(2)=3$
Vertex: $(2,3)$
Opens upward
$x=0$
$f(x)=2x^2-8x+11$
$f(0)=2*0^2-8*0+11$
$f(0)=2*0-0+11$
$f(0)=0-0+11$
$f(0)=11$
Since the graph is above the x-axis and opens upward, there are no x-intercepts.
y-intercept: 11
