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I'm looking to derive the error of a quadratic equation as a function of x.

y=ax^{2}+bx+c

y is measured and variables a,b,c have an associated error Da,Db,Dc

To solve for x you complete the square.

[tex]x=&\pm\sqrt{\dfrac{y-c}{a}+\dfrac{b^{2}}{4a^{2}}}\mp\dfrac{b}{2a}[/tex]

If the variables y,c and b had an assoicated error Dy,Dc and Db.

Then the error would be Dx squared would be the sum of partial derivatives with respect to each variable times by the error on the variable all squared?

[tex]\left(\Delta x\,\right)^{2}=\left(\dfrac{\partial x}{\partial a}\Delta a\right)^{2}+\left(\dfrac{\partial x}{\partial b}\Delta b\right)^{2}+...[/tex]

It seems quite hairy to go though and I was curious if anyone knew a better way to do it or anyone else who has done it?

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# Experimental Error on a quadratic

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