1. y = -x² - 4x – 3

2. y’ = -2x – 4 (take the first derivative to calculate the slope of the curve at each value of x)

3. Note that the slope of the curve at the vertex is 0

4. y’ = 0 when x = -2.

5. When x = -2, y = -4 +8 – 3 = 1

6. Vertex is at (-2,1)

Another way to solve this problem is to graph the parabola:

As you can see from the above graph, the vertex is clearly at (-2,1).