Mathematics - Quadratic Equation Question with Solution | TestHub

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

Given ,$p\left(0\right)=1\Rightarrow c=1$

Now,$\left.\begin{array}{c}p\left(1\right)=4\\ p\left(-1\right)=6\end{array}\right]$

$$\begin{gathered} \left.\begin{array}{c}a+b+c =4\\ a-b+ c=6\end{array}\right]\Rightarrow \left.\begin{array}{c}a+b+1 =4\\ a-b+1=6\end{array}\right] \\ \left.\left.\begin{array}{c}a+b =3\\ a-b=5\end{array}\right] \Rightarrow \begin{array}{c} a=4\\ b=-1\end{array}\right] \end{gathered}$$

$p\left(x\right)=4x^2-x+1$

$p\left(-2\right)=16+2+1=19$