Question

What polynomial has a graph that passes through the given points?

(-2, 2) (-1, -1) (1, 5) (3, 67)

Answer 1

simple enough

Answer 2

\[y = c_0+c_1(x-x_1)+c_2(x-x_1)(x-x_2)+c_2(x-x_1)(x-x_2)(x-x_3)\]

Answer 3

\[y = c_0+c_1(x+2)+c_2(x+2)(x+1)+c_2(x+2)(x+1)(x-1)\]
x=-2; c0=2
\[y = 2 +c_1(x+2)+c_2(x+2)(x+1)+c_2(x+2)(x+1)(x-1)\]each constant term gets filled in by progressing to the next point that zeros out the unknowns

Answer 4

x=-1, y=-1
\[-1 = 2+c_1(-1+2)+0\]
\[1 = c_1(1)\]
c1=1

Answer 5

determine the other constants in this manner, then expand it all out as desired

Answer 6

c1=-3 tho :) forgot how to add

Answer 7

you can use excel to check your work

Answer 8

someones getting a bonus check from bill gates hmmmm :)

Answer 9

haha :)