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

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

Question

What polynomial has a graph that passes through the given points?

(-2, 2) (-1, -1) (1, 5) (3, 67)

amistre64 · Answer

simple enough

amistre64 · Answer

$$y = c_0+c_1(x-x_1)+c_2(x-x_1)(x-x_2)+c_2(x-x_1)(x-x_2)(x-x_3)$$

amistre64 · Answer

$$y = c_0+c_1(x+2)+c_2(x+2)(x+1)+c_2(x+2)(x+1)(x-1)$$
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

amistre64 · Answer

x=-1, y=-1
$$-1 = 2+c_1(-1+2)+0$$
$$1 = c_1(1)$$
c1=1

amistre64 · Answer

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

amistre64 · Answer

c1=-3 tho :)  forgot how to add

dumbcow · Answer

you can use excel to check your work

amistre64 · Answer

someones getting a bonus check from bill gates hmmmm :)

dumbcow · Answer

haha :)