Rico is asked to graph a parabola given the equation y=−x2−2x. At which point would he graph the vertex of the parabola?(1 point)

Responses

(1,2)
left parenthesis 1 comma 2 right parenthesis

(−1,2)
left parenthesis negative 1 comma 2 right parenthesis

(−1,0)
left parenthesis negative 1 comma 0 right parenthesis

(−1,1)

1 answer

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)