Let f(x)=−1/4(x+4)2−8 . what is the average rate of change for the quadratic function from x=−2 to x = 2?

So what the question is asking here is for you to find the slope between the two points on the graph of the function. So you will plug in both x= -2 and x=2 and find their respective "y" values.

-1/4*(-2+4)^2-8

-1/4*(4)-8

-1-8=-9      so we have our first point (-2,-9)

-1/4*(2+4)^2-8

-1/4*(36)-8

-9-8=-17   so we have our second point (2,-17)

we then find the slope using rise over run.
negative seventeen minus negative nine over two minus negative two
(-17-(-9))/(2-(-2))
-8/4
-2 is the average rate of change