Question

For the function f(x) = -(x + 1)2 + 4, identify the vertex, domain, and range. (2 points)

The vertex is (-1, 4), the domain is all real numbers, and the range is y ≥ 4.

The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.

The vertex is (1, 4), the domain is all real numbers, and the range is y ≥ 4.

The vertex is (1, 4), the domain is all real numbers, and the range is y ≤ 4.

Answer 1

The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.

Answer 2

The second choice.

Explanation:

f(x) = -(x + 1)^2 + 4

This is a parabola which opens downwards ( because the coefficient of x is negative).

This is the vertex form of a parabola: f(x) = a(x - b)^2 + c where the vertex is at (b, c). So in this case:-

The vertex is at (-1, 4).

The domain is All Real Numbers and the Range is (-∞, 4] (or y ≤ 4)