How do I rotate a parabola from opening up to opening horizontally?

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How do I rotate a parabola from opening up to opening horizontally?

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Answer 1 · 2014-08-22T05:39:09

You can swap $x$ and $y$ to make it open to the right; this is the common one and is known as the inverse relation. Or you can swap $-x$ with $y$ to make it open to the left.

Let's do an example for the inverse relation of $y=x^2+6x+8$ . We start by swapping $x$ with $y$ :

$x=y^2+6y+8$
$x=(y^2+6y)+8$ start completing the square for $y$
$x=(y^2+6y+9)+8-9$
$x=(y+3)^2-1$
$x+1=(y+3)^2$
$+-sqrt(x+1)=y+3$
$-3+-sqrt(x+1)=y$
$y=-3+-sqrt(x+1)$

You will want to notice that the inverse is a relation and not a function because it doesn't pass the vertical line test.

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How do I rotate a parabola from opening up to opening horizontally?

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