Question

How do you tell if a parabola opens left or right$?$

Answer 1

Describing type of parabola:

If the parabola is symmetric about $x$-axis, then we will have square for the variable $y$ in the equation. That means the given parabola will open upward or downward.
If the parabola is symmetric about $y$-axis, we will have square for the variable $x$ in the equation. That means the given parabola will open rightward or leftward.

Now,

If the standard equation of parabola which is symmetric about $x$-axis is in the form ${\mathit{y}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}\mathit{a}\mathit{x}$ then it will open rightward.

If the standard equation of parabola which is symmetric about $x$-axis is in the form ${\mathit{y}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{4}\mathit{a}\mathit{x}$ then it will open rightward.

If the standard equation of parabola which is symmetric about Y-axis is in the form ${\mathit{x}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}\mathit{a}\mathit{y}$ then it will open upward.

If the standard equation of parabola which is symmetric about $y$-axis is in the form ${\mathit{x}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{4}\mathit{a}\mathit{y}$ then it will open downward.

Hence, we can tell if a parabola opens left or right by their standard equations.