Question

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?



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Answer 1

Thanks to the person above I got the answer correct! the answer is -2

Explanation:

Answer 2

-2

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.