What is the smallest distance between the origin and a point on the graph of $y = \frac{1}{\sqrt{2}} (x^2 - 18)?$

Using substitution we can say that x can equal -9sqrt2 as the main goal of using this certain number is to cancel out the 18 as well as making it so that there is a zero that can multiply with 1/sqrt2. 

THUS THE CLOSEST POINT TO ORIGIN IS : (0, -9sqrt2)

The distance between these points (0 , -9sqrt2 ) and (0 , 0 ) will be = 9sqrt2