Identify the point at which the maximum of the square root function \( y=-\sqrt{3 x+6}-1 \) occurs. (1 point) \( (-6,-1) \) \( (-2,1) \) \( (-2,-1) \) \( (-6,1) \)

To determine the point at which the maximum of the square root function \( y=-\sqrt{3 x+6}-1 \) occurs, we first identify the characteristics of the function. The expression inside the square root, \( 3x + 6 \), must be non-negative for the square root to be defined, which gives us \( 3x + 6 \geq 0 \) or \( x \geq -2 \). Next, since the square root function is being negated and shifted downwards by 1, the maximum value occurs at the smallest value of \( x \) within its domain, which is \( x = -2 \). Plugging this into the function: \[ y = -\sqrt{3(-2) + 6} - 1 = -\sqrt{0} - 1 = -1. \] Thus, the maximum point occurs at \( (-2, -1) \). The answer is \( (-2, -1) \).