Answer:
-2
Step-by-step explanation:
The average rate of change from x=a to x=b is the slope of the line between the points (a, f(a)) and (b, f(b)). It can be computed from ...
m = (f(b) -f(a))/(b -a)
Here, you have a=-2, b=2, so the average rate of change is ...
m = (f(2) -f(-2))/(2 -(-2)) = (-17 -(-9))/4 = -8/4
m = -2
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It should be no mystery that the function is evaluated by putting the value of x where x is in the function, then doing the arithmetic.
f(-2) = -1/4(-2+4)^2 -8 = -1/4(2^2) -8 = -1 -8 = -9
f(2) = -1/4(2+4)^2 -8 = -1/4(36) -8 = -9 -8 = -17
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The graph shows the function, the two points of interest, and a line with a slope of -2 between them, confirming our result.
