To find the vertex of the parabola given by the equation \( y = -x^2 - 2x \), we can rewrite the equation in vertex form or use the standard vertex formula.
The standard form of a quadratic equation is \( y = ax^2 + bx + c \). In this case, \( a = -1 \) and \( b = -2 \).
The x-coordinate of the vertex \( x_v \) can be found using the formula:
\[ x_v = -\frac{b}{2a} \]
Substituting the values of \( a \) and \( b \):
\[ x_v = -\frac{-2}{2 \cdot -1} = \frac{2}{-2} = -1 \]
Now, we need to find the y-coordinate of the vertex by substituting \( x_v \) back into the original equation:
\[ y = -(-1)^2 - 2(-1) = -1 + 2 = 1 \]
Thus, the vertex of the parabola is at the point:
\[ (-1, 1) \]
So the correct response is:
(−1, 1)