Well you have that y-int=5 which is a good start
Now let's solve for the vertex form.
y=2x^2-8x+5
y-5=2x^2-8x
y-5=2(x^2-4x)
y-5+8=2(x^2-4+4)
y+3=2(x-2)^2
Thus the vertex is at (2,-3)
Now that you know this, plug in values(-1,0,1,2,3,4,5) to get (15,5,-1,-3,-1,5,15) respectively
