\( 1 \leftarrow \) Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value. \( f(x)=-3 x^{2}-6 x \) The quadratic function has a maximum value. The value is \( \square \).

To determine whether the quadratic function \( f(x) = -3x^2 - 6x \) has a maximum or minimum value, we first observe the coefficient of \( x^2 \). Since it is negative (\( -3 \)), the parabola opens downwards, indicating that there is a maximum value. To find this maximum value, we can use the vertex formula \( x = -\frac{b}{2a} \), where \( a = -3 \) and \( b = -6 \). Plugging in these values, we get: \[ x = -\frac{-6}{2 \times -3} = -\frac{6}{-6} = 1. \] Next, we substitute \( x = 1 \) back into the function to find the maximum value: \[ f(1) = -3(1)^2 - 6(1) = -3 - 6 = -9. \] So, the quadratic function has a maximum value. The value is \( -9 \).