For the function f(x) = -2(x + 3)² - 1, identify the vertex, domain, and range.

Solution:

The given function is

f(x) = -2(x + 3)² - 1

The equation of a vertical parabola in vertex form is

y = a(x - h)² + k

Where (h, k) is the vertex

Parabola opens upwards if a > 0

Parabola opens downwards if a < 0

From the question

Vertex = (-3, -1)

a = -2

-2 < 0 so parabola opens downwards

Domain here is (-∞,∞) which means all real numbers

Range is (-∞, -1]

y ≤ -1 which means all real numbers less than or equal to -1

Therefore, the vertex is (-3, -1), the domain is all real numbers and the range is y ≤ -1.

For the function f(x) = -2(x + 3)² - 1, identify the vertex, domain, and range.

Summary:

For the function f(x) = -2(x + 3)² - 1, the vertex, domain and range is (-3, -1), all real numbers and y ≤ -1.