2 x=a. x=5, A quick review of end behavior will help us with that. There are lots of things to consider in this process. x t+2 Try It \(\PageIndex{18}\): Construct a formula for a polynomial given a description, Write a formula for a polynomial of degree 5, with zerosof multiplicity 2 at \(x\) = 3 and \(x\) = 1, a zero of multiplicity 1 at \(x\) = -3, and vertical intercept at (0, 9), \(f(x) = \dfrac{1}{3} (x - 1)^2 (x - 3)^2 (x + 3)\). x+3 19 f(0). +6 t The solution \(x= 3\) occurs \(2\) times so the zero of \(3\) has multiplicity \(2\) or even multiplicity. )= 2 If the exponent on a linear factor is even, its corresponding zero haseven multiplicity equal to the value of the exponent and the graph will touch the \(x\)-axis and turn around at this zero. (2,0) p x=3. +4x. Graphing Polynomials - In this section we will give a process that will allow us to get a rough sketch of the graph of some polynomials. ( (1,32). x )=4 x=3 We can check whether these are correct by substituting these values for Double zero at we can determine the end behavior of the graph of our given polynomial: Since the degree of the polynomial, 4, is even and the leading coefficient, -1, is negative, then the graph of the given polynomial falls to the left and falls to the right. 2x The graph skims the x-axis and crosses over to the other side. ). . You can get in touch with Jean-Marie at https://testpreptoday.com/. x2 + a
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