Equations of a Parabola with Vertical/Horizontal Axes of Symmetry

y=1/4px^2

Vertical Axis of Symmetry Equation where vertex at (0,0)

(0,p)

Vertical Axis of Symmetry Equation where vertex at (0,0) Focus

y=-p

Vertical Axis of Symmetry Equation where vertex at (0,0) Directrix

x=1/4py^2

Horizontal Axis of Symmetry Equation where vertex at (0,0)

(p,0)

Horizontal Axis of Symmetry Equation where vertex at (0,0) Focus

x=-p

Horizontal Axis of Symmetry Equation where vertex at (0,0) Directrix

y=1/4p(x-h)^2+k

Vertical Axis of Symmetry Equation where vertex at (h,k)

(h, k+p)

Vertical Axis of Symmetry Equation where vertex at (h,k) Focus

y=k-p

Vertical Axis of Symmetry Equation where vertex at (h,k) Directrix

x=1/4p(y-k)^2+h

Horizontal Axis of Symmetry Equation where vertex at (h,k)

(h+p, k)

Horizontal Axis of Symmetry Equation where vertex at (h,k) Focus

x=h-p

Horizontal Axis of Symmetry Equation where vertex at (h,k) Directrix