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# help pls

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What is the smallest distance between the origin and a point on the graph of y=(1/sqrt(2))(x^2-3) ?

Nov 30, 2019

#1
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The smallest distance is sqrt(3): When x = 1, y = sqrt(2).

Nov 30, 2019
#2
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What is the smallest distance between the origin and a point on the graph of y=(1/sqrt(2))(x^2-3) ?

$$y=\frac{1}{\sqrt2}(x^2-3) \\ \sqrt2\;y+3=x^2\\ x^2=\sqrt2\;y+3$$

this is a concave up parabola with the vertex at (0,3)

So what do you think the smallest distance to the origin is?

Dec 1, 2019