the graph represents the function f(x)=x^2+3x+2

To reflect a function across the x axis, we want to turn all the x values that were once positive negative and vice versa. That means we want f(-x), which is: [tex] f(x)=x^2+3x+2 \implies\\
f(-x)=(-x)^2+3(-x)+2 \implies\\
f(-x)=x^2-3x+2 =g(x) [/tex]