Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left bracket, x, comma, y, right bracket(x,y) point.

Question

y=−x^2−6x−18

Answer 1

To find the coordinates of the vertex of the parabola, we need to convert the equation into vertex form which is y = a(x-h)^2 + k.

Given equation: y = -x^2 - 6x - 18

First, we complete the square to rewrite the equation in vertex form.
y = -(x^2 + 6x) - 18
y = -(x^2 + 6x + 9) + 9 - 18
y = -(x + 3)^2 - 9

From the equation above, we can see that the vertex of the parabola is at the point (-3, -9).

Therefore, the coordinates of the vertex of the parabola are (-3, -9).