Question

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

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

Answer 1

Do you have a graph to choose ? or an equation ?

Answer 2

JUST THIS
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 3

maybe the easiest thing is to test each choice.
For example, if you try x= -1 in each equation, do you get y= -1

Answer 4

yes

Answer 5

this is soo confusing =/

Answer 6

for example, for choice A
A. y = -x^3 + 4x^2 + 2x - 2
y = - (-1)*(-1)*(-1) + 4 * (-1)*(-1) + 2*(-1) - 2

you get y = +1 +4 -2 - 2 = +1
and that is not -1
so it's not choice A

Answer 7

There are alternative approaches, but until you have experience with them, they're not easy. I note that you have been given four ponts, all of which supposedly lie on the same graph. The presence of four data points like this means that you'd be trying to come up with your own 3rd order polynomial, obtaining an expression such as this one:\[y=ax^3+bx^2+cx + d\] which has four unknown variables. For each point (x, y), you'd substitute the given values into this polynomial. You'd end up with four equations in four unknowns, which can be solved for a, b, c and d.

Answer 8

so you have to decide how much time and effort you're willing to spend solving this problem as y ou decide upon a method to use.