Question

lf the parabola $y=a{x}^2+bx+c$ passes through the points $(-1,12)$, $(0,5)$, $(2,-3)$ then the value of $a+b+c=$

• A. $5$
• B. $-6$
• C. $0$
• D. $3$

Answer 1

The correct option is C $0$

$f\left(x\right)=a{x}^2+bx+c$

It is given that $f\left(0\right)=5$, $f(-1)=12$ and $f\left(2\right)=-3$

$f\left(0\right)=c=5$ ... $\left(i\right)$

$f(-1)=a-b+c=12$

$\therefore a-b=12-c$

$\because c=5$

$\therefore a-b=12-5$ $=7$ ... $\left(ii\right)$

$f\left(2\right)=4a+2b+c=-3$

$\Rightarrow 4a+2b=-3-c$

$asc=5$

$\Rightarrow 4a+2b=-8$

$\Rightarrow 2a+b=-4$ ... $\left(iii\right)$

Solving $\left(ii\right)$ and $\left(iii\right)$, we get

$a=1$

$b=-6$

Hence, $a=1,b=-6,c=5$

Thus, $a+b+c$ $=1-6+5$ $=0$.