Question

Use successive differences to classify the function represented in the table. Show all your work.

Answer 1

Since the third row is constant, we know that the function h is quadratic. Say h(x) = ax^2 + bx + c. Using h(0) = 2 = a(0)^2 + b(0) + c, h(1) = 5 = a(1)^2 + b(1) + c, and h(2) = 14 = a(2)^2 + b(2) + c, we find a = 3, b = 0, and c = 2, so h(x) = 3x^2 + 2.same as computing a bunch of slopes only the denomintor is always so just the difference in the numerators −10+29=19 −3+10=7 −2+3=1 −1+2=1 6+1=7 25−6=19 the recessive differences are quadratic, to the original function is "other" namely cubic y=x^3−2 will work if you try the pairs