# How can I tell whether a horizontal parabola opens to the left or the right?

Sep 13, 2014

The same way you tell if a parabola opens up or down, by the leading coefficient of the variable.

Since the $x$-axis is positive to the right, a positive leading coefficient (3) means it opens to the right. eg.

$y = \pm \sqrt{3 x - 4} + 3$

And a negative leading coefficient (-2) means it opens to the left.

$y = \pm \sqrt{4 - 2 x} + 2$

Note that only the top halves of the parabolas are drawn.