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: 2

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.