graph

[Guest]

y=x^2(x-6)^2

 

[soroban]

Hello, batticaloa!

Do you know anything about intercepts?

Graph: \(\displaystyle \,y\:=\:x^2(x\,-\,6)^2\)

We can see that it has x-intercepts at \(\displaystyle x\,=0\) and \(\displaystyle x\,=\,6\).

Since those factors have even powers, the curve is tangent to the x-axis there.
\(\displaystyle \;\;\)(If they were odd powers, the graph simply "cuts through" the x-axis.)

Take a value of \(\displaystyle x\) greater than 6.

At \(\displaystyle x\,=\,7:\;y\:=\:7^2(7\,-\,6)^2\:=\:+49\) . . . the graph is above the x-axis.

This is enough information to make a rough sketch of the graph.

        *     |                  *
              |     * *
         *    |   *    *       *
          *   |  *      *     *
        -----***----------***------
              0            6

 

[stapel]

y=x^2(x-6)^2

From your subject line, I will assume that you are supposed to graph this (rather than find the intercepts or such). At what point in the process are you stuck?

Please reply with specifics.

Thank you.

Eliz.

 

[Guest]

thanks.I understand.