Graphing x=y-y^2: A Guide to Understanding and Visualizing the Equation

  • Thread starter ACLerok
  • Start date
  • Tags
    Graphing
In summary, to graph x=y-y^2, you would plot a parabola with a vertex at (0.75, 0.5) that crosses the x-axis at x = 0 and the y-axis at y = 0 and y = 1. To graph it using a graphics calculator, you can either interchange the labels x and y and plot the equations, or solve for y in terms of x and plot the two resulting equations.
  • #1
ACLerok
194
0
graph this please?

How do I graph x=y-y^2? what would it look like? my calc is extremely rusty so if you can help me out, that'd be great. Thanks!
 
Physics news on Phys.org
  • #2
It's a parabola with a vertex at (0.75, 0.5). It crosses the x-axis at x = 0 and it crosses the y-axis at y = 0 and y = 1. Can you take it from there?
 
  • #3
I don't get the vertex that Tide did.
The "base" parabola, of the form x=y2 (or y= x2) has vertex at (0,0) because if x is not 0, x2 is positive and not below 0. x=y-y2 is not a "perfect square" but you can complete the square: x= -(y2- y+ 1/4) +1/4 (half of the coefficient of y is -1/2 and the square of that is 1/4 so I add and subtract 1/4. When I take the -1/4 out of the parentheses, it is multiplied by that leading -1). The point of that is that -(y2- y+ 1/4)= -(y- 1/2)2, a perfect square.
We now have x= -(y- 1/2)2+ 1/4. If y= 1/2, then x= 1/4 (not 3/4). If y is any other number, (y-1/2)2 is positive so -(y-1/2)2 is negative and x is less than 1/4. The vertex is (1/4, 1/2). Of course, its easy to see, since x= y- y2= y(1- y), that if y= 0 or 1, x is 0. Knowing that the parabola passes through (0,1), (1/4,0), and (0,0) and x is never larger than 1/4 should make it easy to draw.
 
  • #4
Note to self: [itex]\frac {1}{2} - \frac {1}{4} = \frac {1}{4}[/itex]

(Thanks, Halls!)
 
  • #5
how would i enter this in a graphics calculator to graph it?
 
  • #6
There are two ways to do that

(a) Interchange the labels x and y and enter them into your calculator recognizing that the x-axis on your display is really the y-axis and likewise for the y axis.

(b) Solve your original equation for y in terms of x and plot each of the two equations on the same graph.
 
  • #7
Tide said:
There are two ways to do that

(a) Interchange the labels x and y and enter them into your calculator recognizing that the x-axis on your display is really the y-axis and likewise for the y axis.

(b) Solve your original equation for y in terms of x and plot each of the two equations on the same graph.

so if i use option b, i graph y=x and y=1-x ?
 
  • #8
No, you solve the quadratic equation [itex]y^2-y + x = 0[/itex] for y and plot the two y's that you get from that.
 

1. What is the purpose of graphing x=y-y^2?

The purpose of graphing x=y-y^2 is to visually represent the relationship between the two variables, x and y. It allows us to observe patterns and trends in the data and make predictions about the behavior of the variables.

2. How do you plot points for x=y-y^2?

To plot points for x=y-y^2, choose values for x and then use the equation to calculate the corresponding values for y. For example, if x=1, then y=1-1^2=0. Plot this point on the graph as (1,0). Repeat this process for different values of x to get multiple points and then connect them to create the graph.

3. What does the shape of the graph x=y-y^2 tell us?

The shape of the graph x=y-y^2 is a parabola. This tells us that the relationship between x and y is quadratic, meaning that as x increases, y decreases at an increasing rate.

4. How can we determine the maximum or minimum point on the graph?

To determine the maximum or minimum point on the graph x=y-y^2, we can use the formula x=-b/2a, where a and b are the coefficients of the quadratic equation. In this case, a=1 and b=-1, so the maximum/minimum point occurs at x=-(-1)/2(1)=1/2. Plugging this value back into the equation, we get y=1/2-1/2^2=-1/4. Therefore, the maximum/minimum point is (1/2, -1/4).

5. Can we graph x=y-y^2 on a standard x-y coordinate plane?

Yes, we can graph x=y-y^2 on a standard x-y coordinate plane. The x-axis will represent the values for x and the y-axis will represent the values for y. The points can be plotted and connected to create a parabola shape, which can then be interpreted and analyzed based on the trends and patterns shown on the graph.

Similar threads

  • Introductory Physics Homework Help
Replies
10
Views
587
  • Introductory Physics Homework Help
Replies
19
Views
1K
Replies
44
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
477
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • General Math
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
1K
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
900
  • Introductory Physics Homework Help
Replies
2
Views
916
Back
Top