Answer
$y=2(x-2)^2+3$
Work Step by Step
Use vertex form of a parabola:
$$y=a(x-h)^2+k$$
Where vertex is at $(h,k)$.
Substitute vertex $(2,3)$:
$$y=a(x-2)^2+3$$
Now substitute one of the point on the parabola $(1,5)$:
$$5=a(1-2)^2+3$$
$$5=a(-1)^2+3$$
$$5=a+3$$
$$a=2$$
So, equation becomes:
$$y=2(x-2)^2+3$$
