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

 May 16, 2023
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The graph of y=1/sqrt(2)​(x^2−18) is a parabola that is symmetric about the y-axis. The origin is the midpoint of the parabola, so the smallest distance between the origin and a point on the graph is the distance to the vertex.

The vertex of the parabola is at (0,−9/sqrt(2)​), so the smallest distance is sqrt((0−0)2+(−9/sqrt(2)​)^2​) = 9/sqrt(2) = 9*sqrt(2)/2​​.

 May 16, 2023

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