Question

If the parabola $y=a{x}^2+bx+c$, passes through the points $(0,3),(1,-4)$ and $(-1,4)$, then $c-(a+b)=$

Answer 1

Since, It passes through points.
So, $y=a{x}^2+bx+c$ will satisfy the points $(0,3),(1,-4)$ and $(-1,4)$.

$\Rightarrow c=3\cdots \left(i\right)$

$\Rightarrow a+b=-7\cdots \left(ii\right)$

$\Rightarrow a-b=1\cdots \left(iii\right)$
solving the equations, we get
$a=-3,b=-4$ and $c=3$
$\therefore c-(a+b)=10$