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.
A polynomial is a mathematical expression consisting of variables and coefficients, with only the operations of addition, subtraction, and multiplication. It is written in the form of ax^n + bx^(n-1) + ... + cx + d, where a, b, c, and d are constants and n is a non-negative integer.
The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 3x^2 + 5x + 2, the degree is 2 since it is the highest power of x.
There are four main types of polynomials: monomial, binomial, trinomial, and multinomial. A monomial has only one term, a binomial has two terms, a trinomial has three terms, and a multinomial has more than three terms.
The most common forms of polynomials are standard form, factored form, and expanded form. Standard form is written in descending order of powers, factored form shows the polynomial as a product of its factors, and expanded form is the expanded version of the polynomial expression.
Some of the main characteristics of polynomials include: the degree, leading coefficient, constant term, number of terms, and the roots or solutions. These characteristics can help determine the behavior and properties of the polynomial function.