How does the value of a in the function affect its graph when compared to the graph of the quadratic parent function? g(x)=-4x^2 In what ways is the graph of g(x) different from the graph of the parent function?Select all that apply. A. The graph of g(x) is narrower. B. The graph of g(x) is wider. C. The graph of g(x) opens upward. D. The graph of g(x) opens downward.

The function \( g(x) = -4x^2 \) is a transformation of the quadratic parent function \( f(x) = x^2 \).<br /><br />- The coefficient \( a = -4 \) affects the graph in two ways:<br /> 1. **Narrowness/Wideness**: Since the absolute value of \( a \) is greater than 1 (\(|-4| > 1\)), the graph of \( g(x) \) is narrower compared to the parent function.<br /> 2. **Direction**: The negative sign in front of the 4 indicates that the graph opens downward.<br /><br />Therefore, the correct options are:<br />A. The graph of \( g(x) \) is narrower.<br />D. The graph of \( g(x) \) opens downward.