Ineed to know the vertex, intercepts, and range for this problem g(x)=2x^2-8x+6

The range of a quadratic function is:

So the range of is .

x-intercepts:


y-intercepts:

First write g(x)=2x²-8x+6 as 2(x-2)²-2 
g(x)=2(x-2)²-2 
We can say that (x-2)² is always positive and y must has a min. value in vertex.
y=2(x-2)²-2 
(x-2)² min value is 0 so x=2 
y=-2 
Thus its vertex is (2,-2)
For its range 
(x-2)² always positive so (x-2)²=0 and x=2 and y=-2 so we can say that it goes ∞ and it end -2. 
It's range (-2,∞).Because its vertex point is(2,-2) 
Intercepts:
 For y intercepts ,x=0
y=6 
For x intercepts,y=0 
0=2(x-2)²-2 
1=(x-2)²
x-2=1 or x-2=-1 
x=3   or x=1