Parabolas: Standard Form

Vertical:

y = a (x - h)² + k

If a is positive the parabola opens up

If a is negative the parabola opens down

|a| = 1 normal width

|a| > 1 narrow width (vertical stretch)

|a| < 1 wider width (vertical shrink)

vertex (h, k)

axis of symmetry: x = h

The vertex is the midpoint between the focus and the directrix.

Horizontal:

x = a (y - k)² + h

If a is positive the parabola opens right

If a is negative the parabola opens left

|a| = 1 normal width

|a| > 1 narrow width (horizontal stretch)

|a| < 1 wider width (horizontal shrink)

vertex (h, k)

axis of symmetry: y = k

The vertex is the midpoint between

the focus and the directrix.