Question

Image.

Answer 1

*Never mind. The x intercepts were right, but not the y-intercept.

Answer 2

What are the functions provided?

Answer 3

cubic?

Answer 4

If you insist,
A:-1/2(x-3)(x+2)
B:1/6(x-3)^2(x+2)
C:1/4(x+3)(x-2)^2
D:-1/4(x+3)(x-2)^2
E:1/2(x-3)^2(x+2)

Answer 5

We know it should be zero at -2 and 3.

Answer 6

So it has to have x+2 and x-3

Answer 7

When you set x=0, you should have some value near 3

Answer 8

Set x=1 then you have a value near 2

Answer 9

How would you do it if there were no answer choices?

Answer 10

Well, there are infinite solutions technically. You don't even know that it is a polynomial.

Answer 11

If they asked for an approximate equation?

Answer 12

One thing you could do is assume it is an n-degree polynomial and set up a matrix

Answer 13

suppose it was degree 5

Then we have:
y = ax^5 + bx^4 + cx^3 + dx^2+ ex + f

Answer 14

Given 5 different points (x,y), we could come up with 5 equations.

Answer 15

Then it just because a matrix solving for the coefficients.

Answer 16

Okay.