Answer
$(y-1)^2=x$
Work Step by Step
If the major axis of the parabola is parallel to the y-axis then it is in the form of $4k(y-a)=(x-b)^2$, where $(b,a)$ is the vertex of the parabola and $k$ is a constant (positive if open up, negative if open down).
If the major axis of the parabola is parallel to the x-axis then it is in the form of $4k(x-a)=(y-b)^2$, where $(a,b)$ is the vertex of the parabola and $k$ is a constant. (positive if open right, negative if open left).
Here the major axis is parallel to the x-axis and the vertex is in $(0,1)$.
Thus the equation becomes $(y-1)^2=4k(x-0)\\(y-1)^2=4kx$.
We also know that $(1,2)$ is on the graph, hence plugging in $x=1,y=2$ gives us: $(2-1)^2=4k(1)\\1=4k\\k=\frac{1}{4}$.
Hence our equation: $(y-1)^2=4\frac{1}{4}x\\(y-1)^2=x$
