I can provide a clear and concise answer to your question about the graph of the equation y = -|x + 3|.
1. The given equation y = -|x + 3| represents a V-shaped graph that opens downwards due to the negative sign outside the absolute value function.
2. To graph y = -|x + 3|, you first need to consider the graph of y = |x|, which is a V-shaped graph opening upwards with its vertex at the origin.
3. The transformation y = -|x + 3| is a reflection of y = |x| over the x-axis followed by a horizontal shift of 3 units to the left.
4. The vertex of the graph will now be at the point (-3, 0) due to the shift of 3 units to the left.
5. The graph will open downwards and have its lowest point at the vertex (-3, 0) with the arms of the V-shape extending to the left and right from this point.
6. This graph represents the equation y = -|x + 3|.
