help with functions! (last given answer was incorrect.) Thanks!

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

Guest Oct 11, 2021

Guest · Answer 1 · 2021-10-11T05:52:20

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

Alan · Answer 2 · 2021-10-12T04:08:59

This graph should help

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