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 y2-1
The vertex is (3,-1), the domain is all real numbers, and the range isys-t.
O The vertex is (-3, -1), the domain is all real numbers, and the range is ys-1
The vertex is (-3, -1), the domain is all real numbers and the range isy 2-1

Answer 1

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

Explanation:

The general vertex form is f(x) = a(x - b)^2 + c where the vertex is (b, c).

So for f(x) = -2(x + 3)^2 - 1 the vertex is (-3, -1).

Because of the negative coefficient of x^2 ( -2) the parabola opens downwards and the maximum value is -1. So the range is y ≤ -1.

The domain is all real numbers.