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 Question from Krizhia: How is y= 1/2 * (x-1)² be x= √2y + 1. Please show me the steps

Hi,

You need to rearrange this equation so that $x$ is alone on the left side and the right side has no $x.$ I would first multiply both sides by 2 to eliminate the fraction. Thus, multiplying both sides by 2 the equation becomes

$2y = (x-1)^{2}.$

If you now take the square of both sides you get

$\sqrt{2y} = \sqrt {\left( x-1 \right)^2} = \pm (x-1).$

Hence I get two equations

$\sqrt{2y} = x-1 \mbox{ and } \sqrt{2y} = -(x-1) = 1-x.$

Hence either

$x = \sqrt{2y} + 1$

or

$x = 1 - \sqrt{2y}.$

Penny

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