find directix
reemember that the vertex is equal distance from the directex as from the focus
and the directex and focus are on oposite sides of theh vertex
we seee that the directix is to the left of the vertex and focus
equation is
4p(x-h)=(y-k)^2 since the parabola opesn sideways
p is positive
p=distance from vertex to focus
distance is 2 since 3 to 5 is 2
8(x-h)=(y-k)^2
(h,k) is center
(3,3) is center
8(x-3)=(y-3)^2 is the equation
ifyo wanted it in terms of y then
square root both sides thena dd 3
[tex] \sqrt{8(x-3)} +3[/tex]=y
remember that [tex] \sqrt{x} =x^{ \frac{1}{2}} [/tex]
y=[tex]8(x-3)^{ \frac{1}{2} }+3[/tex]
