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

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Answer 1 · 2014-09-13T05:03:54

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

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

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

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

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

![Graph of two parabolas with http://equations.](https://useruploads.socratic.org/aAOCEVsJSWiUqXDW37gS_sideways%20parabola.png)

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