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# Coordinates

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

Oct 27, 2021

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

Hello Guest!

$$y=x^2-3\\ y'=2x\\ m= -\frac{1}{2}\\ -\frac{1}{2}x=x^2-3\\ x^2+\frac{1}{2}x-3=0$$

$$x=-0.25\pm \sqrt{0.0625+3}\\ x=-0.25\pm 1.75\\ x\in\{-2,1.5\}\\ d_{min}= \sqrt{x^2+y^2}=\sqrt{1.5^2+(-\frac{1}{2}\cdot 1.5)^2}$$

$$d_{min}=1.677$$

The smallest distance is 1.677

!

Oct 28, 2021