Use finite differences to determine if each relation is linear or quadratic. x: -4,-3,-2,-1,0,1,2. Y: 5,0,-3,-4,-3,0,5. Linear or quadratic ?
This relation is quadratic because the differences between consecutive terms in the y values are not constant.
First differences: 5-0 = 5, 0-(-3) = 3, (-3)-(-4) = 1, (-4)-(-3) = -1, (-3)-0 = -3, 0-5 = -5
Second differences: 5-3 = 2, 3-1 = 2, 1-(-1) = 2, -1-(-3) = 2, -3-(-5) = 2
Since the second differences are constant, it is a quadratic relation.