Question

Let f(x)=−1/2(x+2)^2+5 .

What is the average rate of change for the quadratic function from x=−3 to x = 1?

Answer 1

Here are a ton of correct answers. I got a few questions wrong but they still show the correct answer.

Answer 2

Answer: 2

Step-by-step explanation:

The average rate of change is the net change of the function, i.e. final value less initial value, divided by the interval:

f(b) - f(a) f(1) - (f(-3)
average change rate from a to b = ---------------- = ---------------
b - a 1 - (-3)

f(1) = -(1/2) (1 + 2)² + 5 = -(1/2) (3)² + 5 = 5 - 9/2 = 1/2

f(-3) = -(1/2) ( -3 + 2)² + 5 = -(1/2) (-1)² + 5 = 5 - 1/2 = 9/2

(1/2) - (9/2)
average change rate = -------------------- = 2
1 - 3
That is the answer.