Question

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

A. The vertex is (3, -1), the domain is all real numbers, and the range is y ≥ -1.

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

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

D. The vertex is (-3, -1), the domain is all real numbers, and the range is y ≥ -1.
2.

Answer 1

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

Explanation:

we have

`f(x)=-2(x+3)^2-1`

This is the equation of a vertical parabola written in vertex form open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The vertex is the point (-3,-1)

The domain is all real numbers

The range is the interval (-∞,-1]

`y\leq -1`