Write down the formula to linearize a function $f(x)$ around an operating point $x_0.$ Also, linearize $f(x)=x^2+3sin(x)$ around $x_0=0.(10$ points$)$

Is $y=a{x}^2+bx+c$ linear in $x$ when $($a$)a=0$ and $($b$)a0,$ where $b$ and $c$ are constants?

$(10$ points$)$