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)

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