Finding the Point of Intersection: Y=x+6 and Y=x^3

In summary, to find the point of intersection between y=x+6 and y=x^3, you need to solve the equation x^3 - x - 6 = 0 by trying the divisors of the constant term, which are 1, 2, 3, 6, -1, -2, -3, -6. After trying different values, the correct point of intersection is (2, 8). You can also use a graphing calculator to plot the two equations and visually see where they intersect.
  • #1
teng125
416
0
may i know how to find the point of intersection between y=x+6 and y=x^3 ??
 
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  • #2
See for what values of x, the y values are the same, so solve:

[tex]x^3 = x + 6 \Leftrightarrow x^3 - x - 6 = 0[/tex]

Divisors of the constant term (6) are possible zeroes.
 
  • #3
ya,but then from x^3 - x - =0 how to solve pls
 
  • #4
ya ,from x^3 -x - 6 = 0
 
  • #5
You TRY SOMETHING!

Have you even tried plugging in numbers to get an idea of how large the solutions should be?
 
  • #6
And as I said, you should try the divisors of the constant term, if you're looking for integer zeroes.
 
  • #7
http://www.sosmath.com/algebra/factor/fac11/fac11.html

Scroll down to "solving the depressed cubic" because that is the form you have.

Though indeed, it is easier to look for an integer solution as TD said, and you can see graphically from the original problem that there are no other solutions.
 
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  • #8
You can always plot the 2 functions to get an idea where the intersection is.
 
  • #9
the answer is it = to 6 and zero??
 
  • #10
teng125 said:
the answer is it = to 6 and zero??
Try graphing the two equations as suggested by others. I graphed it on an online graphing calculator and can see that the two curves intersect at only one point. Remember that intersections are points on the x-y plane, so they should have the form (x,y), not just single numbers. Example: The curves intersect at (1,3) and (5,2).
 
  • #11
i have already drawn it but i can't find the point using the eqn above so i ask for help in this forum
 
  • #12
try to put divisors of 6 , 1,2,3,6 and -1,-2,-3,-6 in the equation(x^3 -x - 6 = 0)
1^3 - 1 - 6 = -6 wrong , I continue 2^3 - 2 - 6 = 8 - 8 = 0 Bingo
the 2 graphs intersect at (2,8).usualy when u have such equation you should what TD told u to do.
 
  • #13
okok got it thanx
 

FAQ: Finding the Point of Intersection: Y=x+6 and Y=x^3

What is the point of intersection between the equations Y=x+6 and Y=x^3?

The point of intersection between Y=x+6 and Y=x^3 is where the two equations intersect or have the same solution. In this case, the point of intersection is (3, 9).

How do you find the point of intersection between two equations?

To find the point of intersection between two equations, you can use the substitution or elimination method. In this case, you can set the two equations equal to each other and solve for x, then plug the value of x into either equation to find the corresponding y value.

Is there only one point of intersection between Y=x+6 and Y=x^3?

Yes, there is only one point of intersection between two equations. This is because two equations can only have one solution or point of intersection where they are equal.

Can you graph the equations Y=x+6 and Y=x^3 to find the point of intersection?

Yes, you can graph the equations Y=x+6 and Y=x^3 and find the point of intersection by looking at the point where the two lines intersect. However, this method may not be as accurate as solving algebraically.

What does the point of intersection represent in the context of these two equations?

The point of intersection represents the solution or values of x and y that make both equations true. It is the point where the two lines cross each other on a graph or the coordinates where the two equations are equal.

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