The average rate of change is equivalent to the slope of the line connecting the two points. At x = 1, y = -3 (the vertex of the parabola). Meanwhile, at x = 3, y = 1. Therefore our two points are (1, -3) and (3, 1). To get the slope between the points, we use the equation m = (y2 - y1)/(x2 - x1) = (1 - (-3))/(3 - 1) = 4/2 = 2.
Therefore the average rate of change between x = 1 to x = 3 is 2.
