# parabola equation

• Jun 5th 2010, 06:35 PM
rosana
parabola 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 PM
11rdc11
Quote:

Originally Posted by 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.

\$\displaystyle y=(4y-y^2)^2\$

Now expand and solve
• Jun 5th 2010, 07:17 PM
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?
• Jun 5th 2010, 07:51 PM
11rdc11
Quote:

Originally Posted by 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?

Use the Intermediate Value Theorem
• Jun 5th 2010, 08:53 PM
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?
• Jun 5th 2010, 09:21 PM
11rdc11
Quote:

Originally Posted by 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?

College Algebra Tutorial on Zeros of Polynomial Functions, Part II