Find the third degree polynomial whose graph is shown in the

figure.

choices are

f(x) = x^3 - x^2 - 2x + 2

f(x) = 1/4(x)^3 - 1/2(x)^2 - x+2

f(x) = 1/4(x)^3 -1/4(x)^2 + 2x + 2

f(x) = 1/2(x)^3 - 1/2(x)^2 - x + 2

Results 1 to 6 of 6

- June 16th 2007, 07:09 PM #1

- Joined
- Jun 2007
- Posts
- 24

- June 16th 2007, 08:09 PM #2

- Joined
- Jun 2007
- Posts
- 24

- June 16th 2007, 08:16 PM #3

- June 16th 2007, 08:27 PM #4
the answer is the second one:

Why did i choose this one? it has all the desired features:

and

The first graph i suggested had the correct x-intercepts and shape, but the y-intercepts were off. if you divide the original graph i suggested by 4, you would get the above graph

to refresh your memory, i suggested , our answer has to be that graph, or some constant times that graph, as the above is. do you see why?

- June 16th 2007, 08:48 PM #5

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 11,547
- Thanks
- 539

Hello, wvmcanelly!

Find the third degree polynomial whose graph is shown in the figure.

The graph has an x-intercept at -2.

. . The function has a factor of:

The graph is tangent to the x-axis at 2.

. . The function has a factor of:

The cubic is of the form: .

Since is on the graph,

. . we have: .

Therefore: . . .Answer (b)

- June 16th 2007, 08:51 PM #6