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

C. The vertex is , the domain is all real numbers, and the range is .

Step-by-step explanation:

We have been given a function . We are asked to identify the vertex, domain and range of the given function.

We can see that our given parabola is in vertex form , where represents vertex of parabola.

We can rewrite our given equation as:

Therefore, the vertex of our given parabola would be .

We know that parabola is a quadratic function and the domain of a quadratic function is all real numbers.

We know that range of a quadratic function in form is:

, when and,

, when

Upon looking at our given function, we can see that , which is less than 0, therefore, the range of our given function would be .

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.