Parabola through three points

Text

Find the parabola $y=ax^{2}+bx+c$ through $A(0,3)$, $B(1,2)$, $C(-1,6)$.

Solution

From $A$: $c=3$. From $B$: $a+b+3=2\Rightarrow a+b=-1$. From $C$: $a-b+3=6\Rightarrow a-b=3$. Adding: $2a=2\Rightarrow a=1$, hence $b=-2$. $\boxed{\,y=x^{2}-2x+3\,}$