If the curve y=ax^2+bx+c, x R, passes through the point (1,2) and the tangent line to this…

Question

If the curve $y=ax^2+bx+c$, $x\in\mathbb R$, passes through the point $(1,2)$ and the tangent line to this curve at the origin is $y=x$, then the possible values of $a,b,c$ are

Accepted Answer

Passing through origin (tangent there) gives $c=0$ and $y'(0)=b=1$. Through $(1,2)$: $a+b+c=2\Rightarrow a=1$.

$$a=1,\ b=1,\ c=0.$$

Solutions · 1