Mathematics - Functions Question with Solution | TestHub

$x^2+3x+2=\min \{|x-3|,|x+2|\}$
$\begin{array}{rl}& y=x^2+3x+2\\ & y=x^2+2\left(\frac{3}{2}\right)x+\frac{9}{4}-\frac{9}{4}+2\\ & y={\left(x+\frac{3}{2}\right)}^2-\frac{1}{4}\\ & y+\frac{1}{4}={\left(x+\frac{3}{2}\right)}^2\\ & \Rightarrow \text{ Parabola vertex }\left(\frac{-3}{2},\frac{-1}{4}\right)\end{array}$ $\Rightarrow$ By graph 2 solution possible