To find the gradient of the curve \( y = 9 - 3x^2 \) at the point where \( x = -2 \), we first need to compute the derivative of the function with respect to \( x \). The derivative will give us the gradient of the curve at any point \( x \).
- Differentiate \( y = 9 - 3x^2 \):
\[ \frac{dy}{dx} = 0 - 6x = -6x \]
- Now, we substitute \( x = -2 \) into the derivative to find the gradient at that point:
\[ \frac{dy}{dx} \bigg|_{x=-2} = -6(-2) = 12 \]
Therefore, the gradient of the curve at the point where \( x = -2 \) is \( \boxed{12} \).