# How do you find the equation of the parabola whose vertex is at (1,-2), and that passes through the point (4,16)?

##### 1 Answer

Sep 7, 2015

#### Explanation:

Assuming the parabola is a function in standard position

with vertex at

The general vertex form is

For the given case;

at

Therefore the equation is

**Note**: the general vertex form assumes the parabola is in standard position (e.g. with a vertical axis of symmetry). Infinitely many alternate solutions are possible if this is not the case.

Three such parabolas are shown below: