To find the vertex of the parabola given by the equation \( y = -x^2 - 2x \), we can rewrite it in vertex form or use the vertex formula for a quadratic equation in standard form \( ax^2 + bx + c \).
Here, \( a = -1 \), \( b = -2 \), and \( c = 0 \).
The x-coordinate of the vertex can be found using the formula:
\[ x = -\frac{b}{2a} \]
Substituting the values:
\[ x = -\frac{-2}{2 \cdot -1} = \frac{2}{-2} = -1 \]
Now, to find the y-coordinate of the vertex, substitute \( x = -1 \) back into the equation:
\[ y = -(-1)^2 - 2(-1) = -1 + 2 = 1 \]
Thus, the vertex of the parabola is at the point \((-1, 1)\).
The correct response is:
(−1, 1)