Question

The change in water level of a lake is modeled by a polynomial function, W(x). Describe how to find the x-intercepts of W(x) and how to construct a rough graph of W(x) so that the Parks Department can predict when there will be no change in the water level. You may create a sample polynomial to be used in your explanations.

Answer 1

@phi do you think you can help me out with this question please i tried but it really hard

Answer 2

@phi do you think you can help me with this question

Answer 3

You may create a sample polynomial to be used in your explanations.

I think they want you to make up a polynomial, and then explain how to find where it equals zero.

Answer 4

oh ok

Answer 5

so i had created one \[2x ^{3}+3x ^{2}-x-4\]

Answer 6

i had put one and i had got zero

Answer 7

can you explain what you mean "i had put one and i had got zero "

Answer 8

i had substitute the x with 1 solve the equation and i got zero

Answer 9

oh, ok. that sounds right.

Answer 10

The question asks

Describe how to find the x-intercepts of W(x) and how to construct a rough graph of W(x)

Did you have a lesson on how to find the x-intercepts of a polynomial ?

Answer 11

no not that i remember

Answer 12

Look through your notes, because they want you to explain how to find the x-intercepts of a polynomial. I don't know what they taught you, so you have to look it up.

Also look up the lesson on how to plot polynomials.

Answer 13

i did and its not there

Answer 14

Here is one way
http://tutorial.math.lamar.edu/Classes/Alg/FindingZeroesOfPolynomials.aspx

use the rational root theorem

Answer 15

and use synthetic division

Answer 16

cant i just use the synthetic division

Answer 17

instead of the rational root theorem

Answer 18

and how would i use the synthetic division for this problem

Answer 19

The rational root theorem gives you the "guesses" that might work.
synthetic division is a way to check each of the guesses.

Answer 20

you can use synthetic division to show that x= 1 is a zero.
you will get a remainder of zero, which means x=1 is a zero of your function

also, the answer will be a quadratic which you can try to find the roots of...
(but it won't have any real zeros)

Answer 21

so the formula for the rational root theorem is \[x=\frac{ b }{ c }\]

Answer 22

@phi

Answer 23

this problem is really giving me a headache

Answer 24

the rational root theorem says take the last number (the constant) which is -4
list its factors 1,2,4 <-- call these p

then take the number in front of the highest order term (the number in front of x^3) which is 2
list its factors 1,2 <-- call these q

list all combinations of ±p/q
can you do that ?

Answer 25

yea the factor of 4 is 1*4 2*2

Answer 26

factors of 2 1*2

Answer 27

factor of 1 is 1*1

Answer 28

yes, now list all combinations of 1,2,4 (from the 4)
divided by 1 or 2 (from the 2 in front of x^3)

Answer 29

ok i divided it by 2 and got 0

Answer 30

meant 1

Answer 31

in other words take the first number from the list 1,2,4. it is 1
now take the 1st number from the second list of 1,2, it is 1. write down 1/1 = 1
then the second number from the second list, and get ½
that means the possible roots are -1, +1, -½, + ½

next, we take the 2nd number from the first list: the 2, and divide it by 1 and by 2
to get 2 and 1. that means more possible roots: -2, +2, -1, +1 (but we already got the 1's)
finally do the 4

Answer 32

you know 1 is the root, so we don't have to test all the choices. But you have to explain a way to find the 1... so we use the rational root theorem to get a list of numbers. then test a few... of course, 1 will work.

once you find x=1 works, look at the quotient you got when you did synthetic division

Answer 33

ok i think i got it now

Answer 34

could you help with 1 more last question

Answer 35

please make it a new post.

Answer 36

i already know