Question

Sketch the graph of

Answer 1

\[y^{2}=x(1-x^{2}) \]

Answer 2

i got the value of x...

Answer 3

when y=0,

Answer 4

x(1-x^2)=0
x=0

Answer 5

x=1
x=-1

Answer 6

i'm not sure what to do next...
when i tried using desmos graphing calculator,the shape of the graph looks a bit weird for me... xD
I don't get it...

Answer 7

Yes, you can choose values of x and evaluate the corresponding y values from the relation, one by one. Solving this relation for either x or y might make this task easier.

Don't start with preconceived notions about what's "weird" and what's not when it comes to grahing. Let the facts speak for themselves.

Think: What would you like to hear from me that might help you graph this relation?

Answer 8

okay...

Answer 9

i know how to sketch the graph when the eqn is y=x(1-x^2)
but since there is a y^2 in the eqn, y^2=x(1-x^2)
i'm really not sure how to do... @mathmale

Answer 10

You begin with \[y^{2}=x(1-x^{2})\]

Answer 11

I'd suggest you solve this for y.
Take the sqrt of both sides. Be sure to include the 'plus or minus' sign on the right.
Note that for every x, there will be 2 y-values, not just one.

Answer 12

You could now make up a table, with "x" heading one column and "y= ---- " the other.
Choose x values within the domain of y and find the corresponding y-values.
Note that x cannot take on just any value, but rather a limited set. Why?

Answer 13

okay,let me try...

Answer 14

is it bcoz of the square root which x cannot take on just any value ?

Answer 15

Interesting! Looks as tho' you'll need to choose x values at which y is NOT zero. There are many such values. Try x=(1/2).

Answer 16

That's one limiting factor. You cannot have a negative quantity under the radical sign.

Answer 17

i c... :)

Answer 18

\[y^{2}=x(1-x^{2})\] could be your starting point. Which range of x values are OK and which are not?

Another way to look at this: a square, such as y^2, can NOT be negative.
Thus, x=-1/2 would create a problem.

Figuring out the domain and range of your y= --- would help in your graphing.

Answer 19

value of x=-2,
y=undefined