Question

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.

Answer 1

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

Explanation:

f(x) = −2(x + 3)^2 − 1

The vertex form is

f(x) = a ( x-h) ^2 + k where ( h,k) is the vertex

f(x) = −2(x - -3)^2 − 1

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

The domain is the values that x can take and x can take all real numbers

The vertex is the maximum since a is negative so the range is all values less than -1

y ≤ −1