Question

Find the x and y coordinates.

y=x^3 - 4x
y= -(x + 2)

Please don't tell me the answer. i'd like to know how to work the problem. thanks

Answer 1

These are two different curves or lines in the xy plane. They intersect at specific point(s) which will be places where the values for x and y solve both equations. You can start by setting the two equations equal to each other to find x values where this could be true.

Answer 2

i can't. i have to use substitution or elimination or some other method and i've tried...i'm stuck..

Answer 3

they are two different lines and they are supposed to intersect at what looks like two points maybe..but idk where to go from here

Answer 4

\[y=x^3-4x\]\[y=-(x+2)\]\[x^3-4x=-(x+2)\]\[x^3-4x+x+2=0\]Can you factor this?

Answer 5

yeah thats basically what i did...its the 4x + x thats throwing me off because that won't factor

Answer 6

-4x+x = -3x

Answer 7

You are missing an x^2 term. But this does factor quite neatly.

Answer 8

okay....i already know all that..lol...sorry my brain is fried

Answer 9

okay i found it..careless mistake..i was getting something way different

Answer 10

What I like to do is first think, are there any obvious positive solutions? Are there any obvious negative solutions? Start with the most simple ones (things that divide 2, for example)

Answer 11

i can't think ahead..i just work the problems..i know how to fix a problem not do it in my head..but i'm still getting -x^3 + 4x -2

Answer 12

=x

Answer 13

how does the x go over like that?i'm so confused

Answer 14

Oh, you are not following:
If y = Equation 1
and y = Equation 2
then Equation 1 = Equation 2

Answer 15

thats how i set up...then i moved the 2 over then the negative..

Answer 16

You should have \[0 = -x^3 + 3x-2\]or\[x^3-3x+2=0\] Did you do this?:
\[y=x^3−4x\]\[y=−(x+2)\]\[x^3−4x=−(x+2)\]\[x^3−4x+x+2=0\]\[x^3−3x+2=0\]

Answer 17

yeah...i had plus 4x instead of -4x..woops

Answer 18

do i use synthetic division now?

Answer 19

Okay, so can you factor using the obvious solutions?

Answer 20

(the obvious solutions to try are going to be the plus or minus divisors of 2)

Answer 21

i can't do that with a cubed x..i thought that only worked with squares

Answer 22

Just plug in 1, -1, 2,and -2 into the equation and see if any of them work.

Answer 23

ummm...i think i can handle it from here..thank you...