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

Absrnz May 16, 2023

#1**0 **

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.

Guest May 16, 2023