# How do you graph y=sqrt(x-2)+3?

Jul 28, 2016

See the explanation

#### Explanation:

Suppose there was an unknown value z

Then ${\left(- z\right)}^{2} = {z}^{2} \text{ and } {\left(+ z\right)}^{2} = {z}^{2}$

So $\sqrt{{z}^{2}} = \pm z$
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So in reality we have $y = \pm \sqrt{x - 2} + 3$

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Lets consider the relationship a different way. The above is such that $x$ is the independent variable and y the dependant variable. Suppose we reversed this.

Write as $\sqrt{x - 2} = y - 3$

Squaring both sides

$x - 2 = {y}^{2} - 6 y + 9$

$x = {y}^{2} - 6 y + 11$

If you plotted this then you would have the same graph as
$y = \pm \sqrt{x - 2} + 3$