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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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@froggie: Is my answer below wrong? :( – Babak S. Dec 1 '12 at 10:02
Wasn't my answer good? :) – Babak S. Dec 18 '12 at 14:01

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

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Right! I missed that,thanks :) – egdfd Nov 29 '12 at 15:27
+ Hi, Babak! Hope to see you soon! ;-) – amWhy Apr 16 '13 at 16:16

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