Final answer:
The vertex of the quadratic equation f(x) = -x^2 - 2x - 2 is found using the formula h = -b/(2a) and is at the point (1, -5).
Step-by-step explanation:
The vertex of the quadratic equation f(x) = -x2 - 2x - 2 can be found by using the vertex formula h = -b / (2a) and k = f(h).
In this equation, a = -1, b = -2, and c = -2.
Plugging the values into the formula, we get h = -(-2) / (2 * -1) = 1, and then calculating k by substituting h back into the equation we find k = f(1)
= -(1)2 - 2(1) - 2
= -5.
Therefore, the vertex of the given quadratic equation is at the point (1, -5).