Finding Points of Intersection for Two Functions

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Homework Help Overview

The problem involves finding the points of intersection for two functions represented by the equations 2x + y - 4 = 0 and y^2 - 4x = 0. Participants are exploring methods to solve these equations and clarify their understanding of the relationships between the variables.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various methods to manipulate the equations, including multiplying the first equation by 2 to facilitate elimination of variables. There are questions regarding the derivation of certain forms, such as y = √(-4x), and concerns about the implications of negative values under the square root.

Discussion Status

The discussion is active, with participants sharing their attempts and questioning the validity of certain steps. Some guidance has been offered regarding the manipulation of equations, but there is no explicit consensus on the best approach yet. Participants are exploring different methods and interpretations.

Contextual Notes

There are indications of confusion regarding the signs in the equations and the implications of certain algebraic manipulations. Some participants express doubts about the feasibility of solving the equations through specific methods, such as using the quadratic formula, which leads to irrational numbers.

Mrencko
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Homework Statement


The problem ask for points of intersection of two functions

Homework Equations


1: 2x+y-4=0
2: (y^2)-4x=0

The Attempt at a Solution


My attempt of solution its in a picture attached below...
I get stuck in this two equations
1: ((y^2)/4)+(y/2)-2=0
2: square root(-4x)-2x+4=0
What. Can i do whit that two equations
I ve tried the square formula and given a weir and nonsense result[/B]
 
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Mrencko said:

Homework Statement


The problem ask for points of intersection of two functions

Homework Equations


1: 2x+y-4=0
2: (y^2)-4x=0

The Attempt at a Solution


My attempt of solution its in a picture attached below...
I get stuck in this two equations
1: ((y^2)/4)+(y/2)-2=0
2: square root(-4x)-2x+4=0
What. Can i do whit that two equations
I've tried the square formula and given a weir and nonsense result[/B]
No picture included.

Multiply first equation by 2 then add equations to eliminate x.
 
SammyS said:
No picture included.

Multiply first equation by 2 then add equations to eliminate x.
This is the picture of my work
IMG_20150429_205217774.jpg
 
How do you get ##\ y=\sqrt{-4x}\ ## ? Specifically, where does that negative sign come from in under the radical ?
 
SammyS said:
How do you get ##\ y=\sqrt{-4x}\ ## ? Specifically, where does that negative sign come from in under the radical ?
That was incorrect. Anyway, much simpler is your first suggestion: Multiply first equation by 2 then add equations to eliminate x.

Equivalently, multiply the first equation by 2, then write it as 4x= 8- 2y so that the second equation can be written [itex]y^2- 8+ 2y= 0[/itex] or [itex]y^2+ 2y- 8= 0[/itex].
 
Thanks i will do that, but what is the point of multiply by 2? Dont change the integrity of the next equation?
 
Mrencko said:
Thanks i will do that, but what is the point of multiply by 2? Dont change the integrity of the next equation?
Multiplying an equation by 2 gives an equivalent equation. Right ?If you want to use the method of substitution, it's better to solve one of the equations for x rather than for y. Then substitute that into the other equation. That way you don't take a square root.
 
Last edited:
1430413029701733866861.jpg
 
  • #10
  • #11
What is thw diference between this and the above equation? Pictures i mean
1430413143609922626788.jpg
 
  • #12
Mrencko said:
What is the difference between this and the above equation? Pictures i meanView attachment 82841
Maybe not much? I didn't like the ##\ \sqrt{-4x\ }\ ##. Especially since x had to be positive.What is your ultimate goal here?
 
  • #13
Find the x and y intersections, i think this is finally solved, but my only doubt, if is this is posible to solve trought this equation:((y^2)/4)=(4-y)/2
 

Attachments

  • 14304138321541924722937.jpg
    14304138321541924722937.jpg
    33.2 KB · Views: 429
  • #14
Mrencko said:
Find the x and y intersections, i think this is finally solved, but my only doubt, if is this is possible to solve trought this equation:((y^2)/4)=(4-y)/2
Why not ?
 
  • #15
If i use the quadratic form whit that equation i get, irrational numbers
 
  • #16
Mrencko said:
If i use the quadratic form whit that equation i get, irrational numbers
You shouldn't.

Please show your calculations.
 
  • #17
i went out for vacations, and somehow now its clear for my using the two metods and two equations, i am very grateful for the help, cheers guys :)
 

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