# How do you find the equation of a parabola with vertex at the origin and focus (0, -2)?

Apr 21, 2017

Use the form $y = a {\left(x - h\right)}^{2} + k$ where $\left(h , k\right) = \left(0 , 0\right)$ and $a = \frac{1}{4 f}$ where f is the signed vertical distance from the vertex to the focus, -2.

#### Explanation:

Use the form $y = a {\left(x - h\right)}^{2} + k$ where $\left(h , k\right) = \left(0 , 0\right)$

$y = a {x}^{2}$

$a = \frac{1}{4 f}$

where f is the signed vertical distance from the vertex to the focus, -2.

$a = \frac{1}{4 \left(- 2\right)}$

$a = - \frac{1}{8}$

$y = - \frac{1}{8} {x}^{2}$