Question 803351
A parabola comparable to {{{y^2=x}}}, but the vertex is at (3,2).  


 A standard derivation would typically be {{{y^2=4px}}} in which p is the distance from vertex to directrix and from vertex to focus point.  In your example, {{{4p=1}}}, so {{{p=1/4}}}.


To finish, center is (3,2), focus is at (3.25,2) and directrix at {{{x=2.75}}}.  The parabola opens toward the right.



Graphing relies on finding two functions:
{{{y-2=0+- sqrt(x-3)}}}
{{{y=2+- sqrt(x-3)}}}
{{{highlight(y=2-sqrt(x-3))}}} and combine with {{{highlight(y=2+sqrt(x-3))}}}.


{{{graph(400,400,-12,12,-12,12,2-sqrt(x-3),2+sqrt(x-3))}}}