To find the domain of the expression \(-15 \cdot \sqrt{x + 2}\), we need to determine the set of values for \(x\) for which the expression is defined.
The square root function is defined only for non-negative values. Thus, we need the expression inside the square root to be greater than or equal to zero:
\[ x + 2 \geq 0 \]
Now, we can solve this inequality:
\[ x \geq -2 \]
Therefore, the domain of the expression \(-15 \cdot \sqrt{x + 2}\) is:
\[ [-2, \infty) \]
This means that \(x\) can take any value from \(-2\) to positive infinity, inclusive of \(-2\).
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