Find the vertex of the parabola by completing the square.
-$y=-x^{2}-2 x-4$
A) $(-1,-3)$
B) $(1,3)$
C) $(-1,3)$
D) $(-1,-5)$

Question

Quizplus · Accepted Answer

To find the vertex of the parabola, we complete the square for the equation $y = -x^2 - 2x - 4$. First, factor out the coefficient of $x^2$, which is -1: $y = -(x^2 + 2x) - 4$. Then, to complete the square, add and subtract $(\frac{2}{2})^2 = 1$ inside the parenthesis: $y = -(x^2 + 2x + 1 - 1) - 4$. Simplify to get $y = -(x + 1)^2 - 3$. The vertex form of a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Thus, the vertex of the given parabola is $(-1, -3)$.

Find the Vertex of the Parabola by Completing the Square y=−x2−2x−4y=-x^{2}-2 x-4y=−x2−2x−4

Find the Vertex of the Parabola by Completing the Square $y=-x^{2}-2 x-4$