Question

Leahclaire
You are having a conference call with the CEO of a paper company. You have interpreted the number of trees cut down versus profit as the function P(x) = -x4 + x3 + 7x2 - x - 6. Describe to the CEO what the graph looks like. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).

Answer 1

What does all the Even degree polynomials look like vs all the Odd degree polynomials?

Answer 2

I have no idea :(

Answer 3

it will look similar to an upside down second degre parabola, but it will cross the x-axis 4 times from the 4th degree term, so it will look funny in the middle near the origin

Answer 4

which class are you taking?

Answer 5

algebra 2 honors

Answer 6

ok

Answer 7

can you factor that into terms like ( ) ( ) ( ) ( ) = 0

Answer 8

\[-(x^4 - x^3 - 7x^2 + x + 6) = 0\]

Answer 9

Then we can tell the points where the graph crosses the x axis

Answer 10

So using the factored version I can graph it and explain the graph?

Answer 11

another simple point you can find on the graph, is let x=0

y = 0 + 0 + 0 + 0 -6 = -6

the point (0,-6) is on the graph

Answer 12

yeah it will help alot

Answer 13

So how would I describe what the graph looks like?

Answer 14

0 = -(x-3)(x-1)(x+1)(x+2)

Answer 15

when you have it in that factored form, the equation will be true , if any one of those parenthesis equals zero
These are your x axis intercepts, 4 of them

Answer 16

so y = 0, when x = 3 , 1, -1 , -2

Answer 17

and we have the point, (0,-6) from letting x=0, to find the y intercept

Answer 18

the negative out front of the x^4 term says that it opens up down

Answer 19

It will do a zig zag sorta thing in the middle, to cross the x axis 4 times

Answer 20

So the line on the graph crosses the x axis four times..? which are.. 3 , 1, -1 , -2
?