Question

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(−1,0)left parenthesis negative 1 comma 0 right parenthesis(−1,1)left parenthesis negative 1 comma 1 right parenthesis(−1,2)left parenthesis negative 1 comma 2 right parenthesis(1,2)

Answer 1

To find the vertex of the parabola given by the equation \( y = -x^2 - 2x \), we can rewrite the equation in vertex form by completing the square.

1. Start with the equation:
\[
y = -x^2 - 2x
\]

2. Factor out the coefficient of \( x^2 \) from the \( x \) terms:
\[
y = -(x^2 + 2x)
\]

3. Complete the square:
- Take half of the coefficient of \( x \) (which is 2), square it, and add it inside the parentheses. Half of 2 is 1, and squaring it gives us 1.
\[
y = -(x^2 + 2x + 1 - 1) = -((x + 1)^2 - 1)
\]
\[
y = - (x + 1)^2 + 1
\]

4. Now, we can write it as:
\[
y = - (x + 1)^2 + 1
\]
This shows that the vertex of the parabola is at the point \( (-1, 1) \).

Thus, the vertex of the parabola is at the point \( (-1, 1) \).

The correct response is:
\[
\text{(-1, 1)}
\]