Consider the graph of the function f (x) = 2 (x + 3) 2 + 2. Over which interval is the graph decreasing?

Y=2 (x+3) ^2+2

y=2 (x^2+6x+9) + 2

y=2x^2+12x+20

dy/dx=4x+12

The graph is decreasing when dy/dx, which is velocity, is less than zero so:

dy/dx<0 when:

4x+12<0

4x<-12

x<-3

So the graph is decreasing from x = (-oo, - 3)