If \(f(x) = x^2\), then \(-f(x) = -(x^2)\). This means that each of the \(y\) coordinates will have a sign change. So \(y = 4\) would become \(y = -4\), and \(y = -1 ...

A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(f(x) = x^2\) is the same as the graph of \(y = x^2\).