Square Root Function

L2MAEL

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A generic square root function graph looks like this:

$\text{equation:}y=\sqrt{x}$

..just like a sideways half parabola.

The reason why it’s a ‘half’ sideways parabola is because it is a positive square root. If it has a negative square root:

$\text{equation:}y=-\sqrt{x}$

..it’s the direct opposite.

This is because this function originates from the equation:

$y^2=x$

However, if we make y the subject: $y=\pm \sqrt{x}$

If it has a $\pm$, it will not be a function as it fails the VLT.

And in L2 Graphing, we only use functions. Therefore, we only either use a $+$, or a $-$ for rooting so that it remains a function.

In this note, I will call the starting point of the graph the ‘vertex’

This is the generic equation:

$y=a\sqrt{(x-p)}+q$

..where $(p,q)$ is the coordinates for the start of this SQRT function. I call this te vertex/starting point.

This is one of the easiest graphs to use, as this is very straightforward.