Identify the domain of the graph of y = -x² - 6x - 13. All real numbers x ≤ - 4, x ≥ - 6, x ≥ - 2.

Solution:

The domain of a function is all real numbers except where the function is undefined. The domain is (∞, - ∞).

We can write the equation in the vertex form of parabola a (x - h)² + k. The vertex of parabola is (h, k).

By using the method of completing the squares we get, 

y = - x² - 6x - 13

-1(x - 3)² + (- 4).

Since the value of a is negative, the graph of the parabola will open downwards.

The vertex of parabola is (3, - 4).

Hence, the range of the parabola is (3, - 4) to negative infinity that is (- ∞, - 4).

Identify the domain of the graph of y = -x² - 6x - 13. All real numbers x ≤ - 4, x ≥ - 6, x ≥ - 2.

Summary:

The domain of the graph y = -x² - 6x - 13 is (- ∞, ∞) and the range is (- ∞, - 4).