Equations of a parabolas graph Cheat Sheet
Equations of a Parabola: Vertex at (0,0); Focus on Axis; a > 0
| Vertex | Focus | Directdix | Equation | Description |
| (0,0) | (a,0) | x=−a | y2=4ax | Axis of symmetry is the x-axis, opens right |
| (0,0) | (−a,0) | x=a | y2=−4ax | Axis of symmetry is the x-axis,opens left |
| (0,0) | (0,a) | y=−a | x2=4ay | Axis of symmetry is the y-axis,opens up |
| (0,0) | (0,−a) | y=a | x2=−4ay | Axis of symmetry is the y-axis,opens down |
Equations of a Parabola: Vertex at (h,k); Axis of Symmetry Parallel to a Coordinate Axis; a > 0
| Vertex | Focus | Directdix | Equation | Description |
| (h,k) | (h+a,k) | x=h−a | (y−k)2=4a(x−h) | Axis of symmetry is parallel to the x-axis, opens right |
| (h,k) | (h−a,k) | x=h+a | (y−k)2=−4a(x−h) | Axis of symmetry is parallel to the x-axis, opens left |
| (h,k) | (h,k+a) | y=k−a | (x−h)2=4a(y−k) | Axis of symmetry is parallel to the y-axis, opens up |
| (h,k) | (h,k−a) | y=k+a | (x−h)2=−4a(y−k) | Axis of symmetry is the y-axis,opens down |