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Question

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


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Solution

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 y2=4ax then it will open rightward.

If the standard equation of parabola which is symmetric about x-axis is in the form y2=-4ax then it will open rightward.

If the standard equation of parabola which is symmetric about Y-axis is in the form x2=4ay then it will open upward.

If the standard equation of parabola which is symmetric about y-axis is in the form x2=-4ay then it will open downward.

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


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