Question

Given the parabola whose equation is , find the focus and determine if the parabola opens up or down.

Answer 1

The equation of a parabola is:
$y = ax {}^{2} + bx + c$
If a>0, then the parabola opens up;
If a<0, then the parabola opens down.
The coordinates of focus are:
$( - \frac{b}{2a} \: \: \frac{1 - b {}^{2} + 4ac}{4a} )$