# intersection points of 2 curves

• May 3rd 2010, 05:41 AM
wilsnunn
intersection points of 2 curves
Hi everybody, this may be really simple and im just missing the point. But how can you calculate the 2 intersection points of 2 quadratics if one is x^2 and the other is -x^2?

Many thanks

Daniel
• May 3rd 2010, 05:50 AM
masters
Quote:

Originally Posted by wilsnunn
Hi everybody, this may be really simple and im just missing the point. But how can you calculate the 2 intersection points of 2 quadratics if one is x^2 and the other is -x^2?

Many thanks

Daniel

Hi Daniel,

The graph of \$\displaystyle f(x)=x^2\$ is a parabola with vertex at the origin and opening upward.

The graph of \$\displaystyle f(x)=-x^2\$ is a parabola with vertex at the origin and opening downward.

Their obvious intersection is the origin.
• May 3rd 2010, 05:59 AM
e^(i*pi)
Quote:

Originally Posted by wilsnunn
Hi everybody, this may be really simple and im just missing the point. But how can you calculate the 2 intersection points of 2 quadratics if one is x^2 and the other is -x^2?

Many thanks

Daniel

There is only one intersection point - at the origin.

You can find this by setting them equal to each other

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

\$\displaystyle 2x^2 = 0\$

\$\displaystyle x = 0\$
• May 3rd 2010, 08:56 AM
wilsnunn
Quote:

Originally Posted by masters
Hi Daniel,

The graph of \$\displaystyle f(x)=x^2\$ is a parabola with vertex at the origin and opening upward.

The graph of \$\displaystyle f(x)=-x^2\$ is a parabola with vertex at the origin and opening downward.

Their obvious intersection is the origin.

I meant if one was say \$\displaystyle f(x)=x^2-6x+9\$ and the other was \$\displaystyle f(x)=-x^2+7x-11\$

How would you do it then? Sorry I should have mentioned that in the opening thread.

Daniel
• May 3rd 2010, 09:13 AM
piglet
Quote:

Originally Posted by wilsnunn
I meant if one was say \$\displaystyle f(x)=x^2-6x+9\$ and the other was \$\displaystyle f(x)=-x^2+7x-11\$

How would you do it then? Sorry I should have mentioned that in the opening thread.

Daniel

\$\displaystyle f(x) \$ is just another name for y

let \$\displaystyle y = y \$

=> \$\displaystyle x^{2} - 6x + 9 = -x^{2} +7x - 11 \$
=> \$\displaystyle 2x^{2} - 13x + 20 = 0 \$

solve that quadratic for x and find the corresponding y value by subbing x into original equation of curve