Question

question
find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x, y) point.
y = -x² - 9

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex.

Step2: Rewrite given equation

The given equation is \(y=-x^{2}-9\), which can be rewritten as \(y = -1(x - 0)^2 - 9\).

Step3: Identify vertex coordinates

Comparing with the vertex form \(y = a(x - h)^2 + k\), we have \(h = 0\) and \(k=-9\). So the vertex is \((0, -9)\).

Answer:

\((0, -9)\)