Graphing question

Let the point be (x, y)

You want the minimum of

$\sqrt{x^2+y^2}$

and 

$y = \frac{1}{\sqrt{3}} (x^2 - 7 + 2x)$

Substitute y in, then use differentiation to find the minimum value of x

The value is about 1.82843 at x = 1.82843