Answer:
[tex]\large\boxed{f(x)=2(x-1)^2+3}[/tex]
Step-by-step explanation:
The vertex form of a quadratic function f(x) = ax² + bx + c:
[tex]f(x)=a(x-h)^2+k[/tex]
Where (h, k) is a vertex.
[tex]h=\dfrac{-b}{2a},\ k=f(h)[/tex]
We have:
[tex]f(x)=2x^2-4x+5\to a=2,\ b=-4,\ c=5[/tex]
Calculate h and k:
[tex]h=\dfrac{-(-4)}{2(2)}=\dfrac{4}{4}=1\\\\k=f(1)\to k=2(1^2)-4(1)+5=2-4+5=3[/tex]
Finally:
[tex]f(x)=2(x-1)^2+3[/tex]
