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How to draw a y=x^2 - pi^2 graph??

username970964

I know y=x^2 is a parabola but how do you draw a y=x^2 - pi^2 graph?

I already drew y=sinx graph.

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Reply 1

Krollo

Original post by Airess3

I know y=x^2 is a parabola but how do you draw a y=x^2 - pi^2 graph?

I already drew y=sinx graph.

Pi^2 is just a constant. Where will the graph meet the x-axis and y-axis? Plot those points then sketch a parabola through them. :awesome:

Posted from TSR Mobile

Reply 2

username970964

Original post by Krollo

Pi^2 is just a constant. Where will the graph meet the x-axis and y-axis? Plot those points then sketch a parabola through them. :awesome:

Posted from TSR Mobile

The graph meets at 0 and 1 on the x-axis I think.

Reply 3

Notnek

Original post by Airess3

The graph meets at 0 and 1 on the x-axis I think.

That's not right. The graph meets the x-axis when y=0, so solve x^2 - pi^2 = 0 to find the intersection points.

Reply 4

username970964

Original post by Krollo

Pi^2 is just a constant. Where will the graph meet the x-axis and y-axis? Plot those points then sketch a parabola through them. :awesome:

Posted from TSR Mobile

Is cos(1) =1 or 0.5?

Reply 5

TheIrrational

Original post by Airess3

Is cos(1) =1 or 0.5?

Neither...

Reply 6

username970964

Original post by notnek

That's not right. The graph meets the x-axis when y=0, so solve x^2 - pi^2 = 0 to find the intersection points.

So x= 0 and x=pi ?

Reply 7

Kallisto

Entertainment Forum Helper

Original post by Airess3

I know y=x^2 is a parabola but how do you draw a y=x^2 - pi^2 graph?
(...)

Pi is a constant, right? put the values of x in this variable, square the value of x first and after that square the constant pi. Last but not least subtract the squared pi from the squared value of x.

So, where is the problem?

(edited 8 years ago)

Reply 8

TheIrrational

Original post by Airess3

So x= 0 and x=pi ?

Close: x = pi is right, but the x = 0 is not. You want to solve

x^2 - \pi^2 = 0

this has 2 solutions, both are related to pi in some way, you got x = pi, so the other is...

Reply 9

Notnek

Original post by Airess3

So x= 0 and x=pi ?

x=0 is wrong.

0^2- \pi^2 \neq 0

Reply 10

Kallisto

Entertainment Forum Helper

Original post by Airess3

So x= 0 and x=pi ?

If you put x = 0 in the equation y = x^2 - pi^2, you will not get 0 as a result, but -pi^2. x = pi is right, but as x^2 is a square term, there is another solution. Do you see what this solution is?

(edited 8 years ago)

Reply 11

davros

Original post by Airess3

I know y=x^2 is a parabola but how do you draw a y=x^2 - pi^2 graph?

I already drew y=sinx graph.

Can you draw the graphs of

y = x^2 - 1

y = x^2 - 4

y = x^2 - 9

etc?

This question is exactly the same principle :smile:

Reply 12

username970964

Original post by Kallisto

If you put x = 0 in the equation y = x^2 - pi^2, you will not get 0 as a result, but -pi^2. x = pi is right, but as x^2 is a square term, there is another solution. Do you see what this solution is?

Is it -1? I drew a graph.

Reply 13

Kallisto

Entertainment Forum Helper

Original post by Airess3

Is it -1? I drew a graph.

No. What happens to negative values, if they are squared? do you get it now? your equation is y = x^2 - pi^2 = 0...

(edited 8 years ago)

Reply 14

TheIrrational

Original post by Airess3

Is it -1? I drew a graph.

Do you know about differences of two squares?

if you had

y = x^2 - a^2

then

y = (x+a)(x-a)

so this graph would cross the x axis at a and -a.

Try applying this method to your problem.

Reply 15

username970964

Original post by TheIrrational

Do you know about differences of two squares?

if you had

y = x^2 - a^2

then

y = (x+a)(x-a)

so this graph would cross the x axis at a and -a.

Try applying this method to your problem.

How would you draw a graph of y=(x+pi)(x-pi) ? I know that'd lead to x=-pi and x=pi but would it still be the same parabola shape?

Reply 16

Notnek

Original post by Airess3

How would you draw a graph of y=(x+pi)(x-pi) ? I know that'd lead to x=-pi and x=pi but would it still be the same parabola shape?

If you expand it you'll get back to a quadratic so it's still a parabola.

It'll be a parabola that goes through x=pi and x=-pi

Reply 17

TheIrrational

Original post by Airess3

How would you draw a graph of y=(x+pi)(x-pi) ? I know that'd lead to x=-pi and x=pi but would it still be the same parabola shape?

Exactly what notnek said above, it would still be a parabola shape which crosses the x-axis and -pi and pi.

Reply 18

username970964

Original post by notnek

If you expand it you'll get back to a quadratic so it's still a parabola.

It'll be a parabola that goes through x=pi and x=-pi

I'm having a bit of a problem drawing this?

Reply 19

Notnek

Original post by Airess3

I'm having a bit of a problem drawing this?

It's looking better but you haven't shown that the parabola crosses the x-axis at pi and -pi. But you have a pi on your y-axis which is not necessary.

Also, the sin graph is upside down and you need to think about where the sin graph crosses the x-axis and match this up with the parabola e.g. sin(x) crosses the x-axis at x=pi and so does the parabola.