# parabola equation

#### rosana

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.

#### 11rdc11

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

#### rosana

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?

#### 11rdc11

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

#### rosana

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?

rosana