Question

LAST ONE!
You are having a meeting with the CEO of a technology company. You have interpreted the number of laptops produced versus profit as the function P(x) = x4 − 3x3 − 8x2 + 12x + 16. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. 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

@Mehek

Answer 2

You do the same thing where you factored or used the quadratic formula to solve for x and then found the y-intercept

Answer 3

If you factored this equation it would be P(x)=(x+2)(x-2)(x-4)(x+1) right?

Answer 4

Correct

Answer 5

Solve it step by step:

\[x^4-3x^3-8x^2+12x+16=0\]
Factor
\[(x+1)(x-2)(x+2)(x-4)=0\]
\[x+1=0 \]
\[x=-1\]
\[x - 2 =0\]
\[x=2\]
\[x-4 = 0\]

Answer 6

So when you solve for each x, you get your x-intercepts
That's the first thing you'd plot

Answer 7

Unfortunately I don't know how to add graphs.

Answer 8

https://www.desmos.com/calculator/obgh6o6jkv

Answer 9

wait slow down a bit i just got confused so

Answer 10

once you factor this P(x) = x4 − 3x3 − 8x2 + 12x + 16.

Answer 11

So you got the factored part

Answer 12

you getP(x)=(x+2)(x-2)(x-4)(x+1)

Answer 13

Correct
Now you need to know what each x is equal to

Answer 14

In order to do that, set each of those to 0
(x + 2) = 0
(x - 2) = 0
(x - 4) = 0
(x + 1) = 0

Answer 15

And then you solve for every one of them
For the first one:

x + 2 = 0
x + 2 - 2 = 0 - 2
x = -2

So one x-intercept is at (-2, 0)

Do that for the rest of them

Answer 16

if im thinking correctly
X intercepts (-2,0), (2,0), (4,0), (-1,0)

Answer 17

Yep

Answer 18

ok now what once we have the x intercepts what do we do now?

Answer 19

@Mehek

Answer 20

do i use Quadratic formula

Answer 21

if so then x=-2,2,4,-1

Answer 22

but i dont think thats what we need

Answer 23

@Mehek

Answer 24

@Shadow could you help me since she left T~T

Answer 25

You need the x-intercepts to graph

Answer 26

i already finished sorry i couldnt wait any longer