The function \( g \) is defined as follows. \[ g(x)=-4 x^{2}+3 \] If the graph of \( g \) is translated vertically upward by 3 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. \( h(x)= \) II.

1. The original function is given by \[ g(x) = -4x^2 + 3. \] 2. Translating a function vertically upward by 3 units means adding 3 to the output of the function. Hence, the new function \( h(x) \) is obtained by \[ h(x) = g(x) + 3. \] 3. Substitute the expression for \( g(x) \) into the equation: \[ h(x) = (-4x^2 + 3) + 3. \] 4. Simplify the expression by combining like terms: \[ h(x) = -4x^2 + 6. \] Therefore, the expression for \( h(x) \) is \[ \boxed{-4x^2 + 6}. \]