# In a Nutshell: Parabola Forms

## part of the In a Nutshell series on Adrian’s Study Club

### Factored form `y=a(x-x_1)(x-x_2)`

Given:

- 2 x-ints
- One other point `P(x,y)

### Vertex Form `y=a(x-h)^2 + k`

Given:

- Vertex
`V(h,k)`

`P(x, y)`

### General Form `y=ax^2 + bx + c`

Given:

- 3 points

OR

- 2 points
- y-int where
`y-int = c`

OR

- Axis of symmetry `x=-(b/2a)
- 2 other points

Form | General `y = ax^-2 + bx + c` | Vertex `y =a (x-h)^2 + k` | Intercept `y=(x-x_1)(x-x_2)` |
---|---|---|---|

Axis of symmetry | `x = -(b/2a)` | `x = h` | `x=((x_1 + x_2)/2)` |

Vertex | Sub `x = -(b/2a)` into the equation to find `y` . | `(h, k)` | Sub `x=((x_1 + x_2)/2)` into the equation to find y. |

Form | Vertical Translation `y = ax^2 + c` | Horizontal translation `y=a(x-h)^2` |
---|---|---|

Axis of symmetry | `x=0` (y-axis) | `x=h` |

Vertex | `V(O,c)` | `V(h,0)` |