Question

Which of the following polynomial inequalities has the given graph as a solution?

A) y^3 ≤ 16 y

B) 4y - y^2 ≥ 0

C) y^3 - 16 y ≥ 0

D) y^2 ≥ 4y

Picture attached.

Answer 1

Please help anyone! :(

Answer 2

Looks like you may have to try factoring/simplifying each equation. Try it on each one, simplify it or factor out a y where you can, then you may be able to use a difference of two squares after factoring.

Answer 3

@agent0smith I simplified each equation, but I am not sure if the right answer would be A or C

Answer 4

For A I got y ≤ -4 or 0 ≤ y ≤ 4

Answer 5

For C I got -4 ≤ y ≤ 0 or y ≥ 4

Answer 6

I'd start with these two:

B) 4y - y^2 ≥ 0

C) y^3 - 16 y ≥ 0

B you can factor as \[\large y(4-y) ≥ 0 \]
and C you can factor as \[\large y(y^2 - 16 ) ≥ 0\] and then use a diff. of two squares on that one.

Answer 7

So I am not sure now :(

Answer 8

"For C I got -4 ≤ y ≤ 0 or y ≥ 4"

doesn't this look exactly like the picture? Assuming your work is correct.

Answer 9

So C is correct then?

Answer 10

Wow I can't believe I did it correct :(

Answer 11

@agent0smith

Answer 12

Yep, C looks correct. Graphing confirms it too: https://www.google.com/search?q=y%5E3+-+16+y&aq=f&oq=y%5E3+-+16+y&aqs=chrome.0.57&sourceid=chrome&ie=UTF-8

the points where the line is above the horizontal axis are where it's greater than/equal to zero.

Answer 13

Thank you very much!!! :)