The discussion revolves around sketching the graph of the polynomial function y = x(x - 3)². Participants are exploring the characteristics of the polynomial, including its zeros, end behaviors, and turning points.
Some participants have provided guidance on examining the polynomial near its zeros and suggested considering the behavior of the function in specific intervals. There is an ongoing exploration of the polynomial's shape and characteristics, but no explicit consensus has been reached.
Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply in their analysis.
Veronica_Oles said:Homework Statement
I have to sketch a graph of y=x(x-3)^2
Homework Equations
The Attempt at a Solution
I know that the zeros are 0 and 3. The part which confuses me is that end behaviours as well as turning points. I am unsure of which way the end behaviours should be pointing. Is the highest degree 2 or 3? And how to I know which quadrants it should be traveling to and from?
I understand it now.Mark44 said:To expand on what Ray said concerning the x-intercepts, when x is "close to 0" the graph is "close to" y = x(0 - 3)2 = 9x. In other words, near x = 0, the graph of your polynomial looks a lot like the graph of the line y = 9x.
When x is "close to" 3, the graph of your polynomial resembles y = 3(x - 3)2, a parabola. I'm hopeful that you have a good idea about the shape of this parabola.
If you expand x(x - 3)2, it should be obvious what the degree of this polynomial is.