The function \( f \) is defined as follows. \[ f(x)=-3 x^{2}-3 \] If the graph of \( f \) is translated vertically, downward by 4 units, it becomes the graph of a function \( h \). Find the expression for \( h(x) \). Note that the ALEKS graphing calculator may be helpful in checking your answer. \( h(x)=\square \)

We are given the function \[ f(x)=-3x^2-3. \] A vertical translation downward by 4 units means we subtract 4 from the function. Thus, the translated function \( h(x) \) is given by \[ h(x)=f(x)-4. \] Substitute the expression for \( f(x) \): \[ h(x)=-3x^2-3-4. \] Combine the constant terms: \[ h(x)=-3x^2-7. \] Therefore, the expression for \( h(x) \) is \[ \boxed{-3x^2-7}. \]