Solution
For this case the general equation of a parabola is given by:
[tex]y-k=a(x-h)^2[/tex]And for this case the vertex is given by:
V= (h= 5, k= 2)
Then replacing we got:
[tex]y-2=a(x-5)^2[/tex]We can use the point given x=6 and y=3 and replacing we got:
[tex]3-2=a(6-5)^2[/tex]And we got a= 1
Then the equation would be:
[tex]y=(x-5)^2+2[/tex]