Hi everyone,

I have a simple question but I can't solve it

what is the intersection point between these two parabola

$\displaystyle y=x^2$

and

$\displaystyle x=4y-y^2$

Thanks for any kind of help.

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- Jun 5th 2010, 06:35 PMrosanaparabola equation
Hi everyone,

I have a simple question but I can't solve it

what is the intersection point between these two parabola

$\displaystyle y=x^2$

and

$\displaystyle x=4y-y^2$

Thanks for any kind of help. - Jun 5th 2010, 06:38 PM11rdc11
- Jun 5th 2010, 07:17 PMrosana
when I expand the equation $\displaystyle y=(4y-y^2)^2$

it will be

$\displaystyle y^4-8y^3+16y^2-y=0$

I know that $\displaystyle y=0$

but what about the other solution of the equation? - Jun 5th 2010, 07:51 PM11rdc11
- Jun 5th 2010, 08:53 PMrosana
I know the meaning of intermediate value theorem is that there is apoint c in interval $\displaystyle [a,b]$ for a function f verifying

$\displaystyle f'(c)=(f(b)-f(a))/(b-a)$

How is this related to the solution of the equation? - Jun 5th 2010, 09:21 PM11rdc11