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?

Answer 1

To find the vertex of the parabola given by the equation \( y = -x^2 - 2x \), we can use the formula for the x-coordinate of the vertex of a parabola in the form \( y = ax^2 + bx + c \):

\[
x = -\frac{b}{2a}
\]

Here, \( a = -1 \) and \( b = -2 \).

Substituting these values into the vertex formula:

\[
x = -\frac{-2}{2 \cdot -1} = \frac{2}{-2} = -1
\]

Now, we need to find the y-coordinate of the vertex by substituting \( x = -1 \) back into the original equation:

\[
y = -(-1)^2 - 2(-1) = -1 + 2 = 1
\]

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

Thus, Rico would graph the vertex of the parabola at the point \( (-1, 1) \).