parabola equation

Apr 2006
20
0
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.
 
Jul 2007
894
298
New Orleans
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.
\(\displaystyle y=(4y-y^2)^2\)

Now expand and solve
 
Apr 2006
20
0
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?
 
Jul 2007
894
298
New Orleans
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?
Use the Intermediate Value Theorem
 
Apr 2006
20
0
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?