How do you find the equation of the parabola whose vertex is at (1,-2), and that passes through the point (4,16)?
Assuming the parabola is a function in standard position
with vertex at
The general vertex form is
For the given case;
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: