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Find $a$, $b$ and $c$ so the line $y=x$ can be a tangent of the parabola $y=ax^2+ bx+c$ at the point $x=1$. The parabola passes from the point $M(-1;0)$. So I formed the system $2a+b=1$ $a-b+c=0$ How do I solve this system?

Details : From $y=x$ we see that $k=1$ (we also have that $x=1$) so $2\cdot a\cdot 1+b\cdot 1=1$

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    Wasn't my answer good? :)2012-12-18

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The parabola and the line intersect each other at $x=1$. This gives you another equation.

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    + Hi, Babak! Hope to see you soon! ;-)2013-04-16