Question

Any help would be great! :)
What polynomial has a graph that passes through the given points?
(-2, 2) (-1, -1) (1, 5) (3, 67)

A. y = -x3 + 4x2 + 2x - 2
B. y = x3 + 4x2 + 2x - 2
C. y = x4 + 4x3 + 2x2 - 2x
D. y = x3 - 4x2 - 2x - 2

Answer 1

since you have choices you can check, otherwise it is hard

Answer 2

That's the problem I don't know how to check or do this problems!

Answer 3

i would try 1 first, because it is easiest
for the first one \[y = -x^3 + 4x^2 + 2x - 2 \] if \(x=1\) you get
\[1-4+2-2=-3\] not \(5\) so that one is out already

Answer 4

\[ (-2, 2) ,(-1, -1), (1, 5) ,(3, 67) \] means:
if \(x=-2\) then \(y=2\)
if \(x=-1\) then \(y=-1\)
if \(x=1\) then \(y=5\)
if \(x=3\) then \(y=67\)

Answer 5

i would plug in 1 in to each of them, and see which one or ones gives 5 as an answer for y
if it does not, get rid of it

Answer 6

i think in this case that is all you have to check, because i think only one of them will give \(y=5\) if you make \(x=1\)