Question

is this polynomial down to the left and down to the right?
f(x) = -(x+2)^3(x-5)^2(x-8)

Answer 1

State the end behavior of the following polynomial:

Answer 2

Are you missing some signs ? The graph seems quite complicated.

Answer 3

no ... it seems complicated to me as well ... =(

Answer 4

here are my options :
A. Up on the left and up on the right ↑ ↑
B. Down on the left and up of the right ↓ ↑
C. Down of the left and down on the right ↓ ↓
D. Up on the left and down on the right ↑ ↓
E. None of the above

Answer 5

This is how the graph looks.

Answer 6

Your function is of degree 6 and the coefficient of x^6 is negative so it is down to the left and down to the right.

Answer 7

ty

Answer 8

This may be of some help: http://www.purplemath.com/modules/polyends.htm

Answer 9

that's a good links thanks

Answer 10

yw.

Answer 11

for the above problem I looked at the last two terms and saw they were both negative so thought that is how you go down to the left and down to the right ....

Answer 12

First we need to find the leading term just like we did before:
f(x) = -(x+2)^3(x-5)^2(x-8)
Take the leading term of each sub-expression:
-(x)^3 * x^2 * x = -(x)^6

It is an even degree polynomial with a negative leading coefficient. Compare it to the graph on the link.

Answer 13

I hope I start really getting these soon ...

Answer 14

Which part you are having difficulty with? Finding the leading term or figuring the up/down thing?

Answer 15

figuring the up and down

Answer 16

Just remember:
x^2 graph is U-shaped. The graph opens up. Both left and right ends are up just like the ends of U.
-x^2 graph is inverted U-shaped. Both left and right ends are down just like the ends of an inverted U.

This can be extended to any EVEN degree polynomial:
If the leading coefficient is positive, both ends up much like x^2
If the leading coefficient is negative, both ends down much like -x^2

Answer 17

so the -(x)^6 is like an inverted U-shape? and they are both down

Answer 18

The graph for x^3 looks like this:
Left end down and right end up.

The graph for x^3 looks like this:
Left end up and right end down.

So for any odd degree polynomial, if leading coefficient is positive, it will behave just line x^3: Left end down and right end up.
if leading coefficient is negative, it will behave just line -x^3: Left end up and right end down.