Answer:
(–∞, –3)
Step-by-step explanation:
The function [tex]f(x) = 2(x + 3) ^ 2 +2[/tex] is a quadratic function of order 2 and positive coefficient.
This is in the form of the function [tex]y = x^2[/tex], but it is displaced 3 units to the left of the x axis and two units up in the y axis. type of functions are decreasing from -∞ to its vertex and then they are increasing from the vertex to infinity.
Observe in the attached graph that this function has its vertex in the point (-3, 2) and is decreasing from -∞ to x = -3. Then it is increasing until ∞. Therefore the correct option is:
(-∞, -3)
