Answer
$f(x)=(x-2)^2+1$.
Work Step by Step
The vertex form of the quadratic function $ax^2+bx+c=0$ can be expressed as $f(x)=a(x-h)^2+k$ and its vertex is at $(h, k)$.
As depicted in the picture, the vertex of the graph is at $(h, k)=(2,1)$, and thus, the quadratic function becomes $f(x)=a(x -2)^2+1$.
Plug in the values $(0,5)$ to obtain:
$5=a(0 -2)^2 +1 \\ 4a+1=5 \implies a=1$
Therefore, the equation of the function can be expressed as: $f(x)=(x-2)^2+1$.
