Answer
Domain of the parabola:$[4,\infty]$
Range of the parabola: $[-\infty,\infty]$
Work Step by Step
In order to plot the graph, use a graphic calculator or give arbitrary numbers to x and evaluate it in the function and plot those points.
For calculating the domain and range of the parabola, we have to identify first where the parabola opens. If opens up or down the domain is $[-\infty,\infty]$ in the same way if opens left or right the range is $[-\infty,\infty]$.
Otherwise we have to calculate the vertex of the parabola in order to get the range of the parabola when open up or down, and if open left or right, to find the domain.
In order to calculate the vertex, let's see the parabola equation:
$$b(x-h)=(y-k)^2$$ where the vertex is $$(h,k)$$
We take the equation to that form by completing squares:
$x=2(y^2-2y+3)$
$x=2(y^2-2y+1-1+3)$
$x=2((y^2-2y+1)+2)$
$x=2(y^2-2y+1)+4$
$x-4=2(y-1)^2$
$\frac{1}{2}(x-4)=(y-1)^2$
Matching the equation:
$\frac{1}{2}(x-4)=(y-1)^2$
$vertex = (4,1)$
As the equation has the form of horizontal axis of symmetry and b>0, the parabola opens right.
As we see in the graph,
Domain of the parabola:$[4,\infty]$
Range of the parabola: $[-\infty,\infty]$