Question 1176544
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Hi

the vertex form of a Parabola opening up(a>0) or down(a<0), 
{{{y=a(x-h)^2 +k}}} 
where(h,k) is the vertex  and  x = h  is the Line of Symmetry , 
the focus is (h,k + p), With Directrix y = (k - p), a = 1/(4p)

y = 2x^2 - 4x + 5 = 2(x-1)^2 -2 + 5 = 2(x-1)^2 +3
 y = 2(x-1)^2 +3
a = 1/(4p) 0r p = 1/4a = 1/8

  V(1,3)  and x = 1 is the Line of Symmetry 

 F( 1, 3.125)   Directrix y = 3 - .125) = 2.875
Wish You the Best in your Studies.
{{{drawing(300,300,   -6, 6, -6, 6,  blue(line(1,10,1,-10))  ,  
 grid(1),

circle(1, 3.125, 0.2),
graph( 300, 300, -6, 6, -6, 6,0, 2.875, 2(x-1)^2 +3))}}}
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