The function \( g \) is defined as follows. \[ g(x)=-2 x^{2}+3 \] If the graph of \( g \) is translated vertically downward by 9 units, it becomes the graph of a function \( f \). Find the expression for \( f(x) \). Note that the ALEKS graphing_calculator may be helpful in checking your answer. \( f(x)=\square \)

To find the expression for \( f(x) \), we start with the original function \( g(x) = -2x^2 + 3 \). Since the graph is translated vertically downward by 9 units, we subtract 9 from the entire function \( g(x) \). So, the new function \( f(x) \) can be expressed as: \[ f(x) = g(x) - 9 \] Substituting \( g(x) \) into the equation gives: \[ f(x) = (-2x^2 + 3) - 9 \] Simplifying this expression results in: \[ f(x) = -2x^2 + 3 - 9 = -2x^2 - 6 \] Therefore, the expression for \( f(x) \) is: \[ f(x) = -2x^2 - 6 \]