Transformations of Quadratic Functions

To reflect $f(x)$ in the $x$-axis we want to move every point on $f(x)$ to the other side of the $x$-axis but with the same distance to it. Note that reflecting a quadratic function puts a negative sign in front of the parent function. Thus, $g(x)=\text{-}f(x)$ where $g(x)$ is the transformed function.