Question

Find the simultaneous equations formed by the condition that the equation $y=a{x}^2+bx+c$ passes through the points $(2,-10)$, $(0,2)$ and $(4,14)$ and then find the value of $a+b+c$.

• A. $6.5$
• B. $7.5$
• C. $6$
• D. $13$

Answer 1

The correct option is A $6.5$

It is given that $y\left(0\right)=2$, $y\left(2\right)=-10$ and $y\left(4\right)=14$

Now $y\left(0\right)=c=2$,

Hence $c=2$

Therefore $y\left(x\right)=a{x}^2+bx+2$

$y\left(2\right)=-10$

Hence $4a-2b+12=0$...(i)

And $y\left(4\right)=14$

Hence $16a+4b+2=0$.

Solving the equations $4a-2b+12=0$ and $16a+4b-12=0$ give us $b=5$ and $a=-0.5$.

Hence, $a+b+c=-0.5+5+2=6.5$