What is the smallest distance between the origin and a point on the graph of \(y=\dfrac{1}{\sqrt{2}}\left(x^2-8\right)\)

By quadratic optimization, the smallest distance between the origin and the graph is $\boxed{2 \sqrt{2}}$.

eek that was incorrect as well..

This graph should help

The smallest distance occurs at x = 0. You should now be able to determine the distance.