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

Plug x = -3 into the function to get a y value.
-(1/2)(-3 + 2)^2 + 5
-(1/2)(1) + 5
-(1/2) + 5 = 4 1/2
(-3, 4 1/2)

Plug x = 1 into the function to get a y value.
-(1/2)(1 + 2)^2 + 5
-(1/2)(9) + 5 = 1/2
(1, 1/2)
Now with two ordered pairs, use the slope formula and find the slope.
(1/2 - 4 1/2) / (1 - -3)
(-4/4) = -1