Find \( g(x) \), where \( g(x) \) is the translation 4 units down of \( f(x)=x^{2} \). Write your answer in the form \( \mathrm{a}(\mathrm{x}-\mathrm{h})^{2}+\mathrm{k} \), where \( \mathrm{a}, \mathrm{h} \), and k are integers. \( g(x)= \)

To translate the function \( f(x) = x^2 \) downward by 4 units, you subtract 4 from the original function. The general form for the translation is: \[ g(x) = a(x - h)^2 + k \] where: - \( a \) is the vertical stretch/compression factor, - \( h \) is the horizontal shift, - \( k \) is the vertical shift. Since we are only translating the graph downward by 4 units, \( a = 1 \), \( h = 0 \), and \( k = -4 \). Plugging these values into the equation gives: \[ g(x) = 1(x - 0)^2 - 4 = x^2 - 4 \] **Answer:** \[ g(x) = x^{2} - 4 \]