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

 

this problem makes my head hurt

i looked around for the solution already, but all that i got were wrong answers and my intructor keeps telling me "If (x, y) is on the graph, how far is it from the origin?" and i dont get it still :((

 

pls someone help before my teacher gives me a bad grade!! thank you so much!!! have a good day <3

 Jul 14, 2022
 #1
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The smallest distance is given by sqrt(65)/3.  Hope this helps!

 Jul 14, 2022
 #2
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thank you so much!! i got the answer :D

 Jul 14, 2022

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