P6 Opener Use the clues to draw a reasonable sketch of a polynomial function Graph III Y-intercept: (0,-8) Only X-intercepts: (-4,0) Bounce (4,0) Bounce Passes through(-6,-6) Passes through (6,-6) What degree could this function be? Why? What do you know about the leading coefficient? Graph IV Y-intercept: (0,5) Only X-intercepts: (-6,0) cross (-1,0) cross (3,0) bounce What degree could this function be? Why? What do you know about the leading coefficient?

Unit: Polynomials Day 6 P6

How will we know if a graph will bounce or cross at that x-intercept How will we know if a graph will bounce or cross at that x-intercept? That seems important so let us explore and figure it out… Desmos P6

Exponent is even Bounces Exponent is odd

Which of the following polynomial functions might have the graph shown? B) C) D)

For the polynomial list the zero and its multiplicity and whether it touches/ bounces or crosses the x axis at each x-intercept. A) B) C) D)

Analyze and Graph each Polynomial Function by Hand Find the x-intercepts and determine if they will bounce or cross at that value. find the y-intercept (0, ___) Complete the table Use the info to design a graph Factor the polynomial and use zpp to find the zeros- x-intercepts. Determine if the graph will bounce or cross. b) find the y-intercept Complete the table d) Use the info to design a graph x y -3 2 x y -4 1 These problems can be for a quiz or Day 3 of this lesson

Solutions

Your zeros are 5 (a double zero- multiplicity 2), -4, and 2 Given the zeros of a polynomial, write the function of least degree with leading coefficient of 1 in factored form. Your zeros are 5, 2, and -4 Your zeros are 5 (a double zero- multiplicity 2), -4, and 2 Your zeros are 3 (multiplicity 2) and 6 (multiplicity 2)

Your zeros are 5 (a double zero- multiplicity 2), and 2 Given the zeros of a polynomial, write the function of least degree with leading coefficient of 1 in factored form and then in standard form. Your zeros are 1, 3, and -4 Your zeros are 5 (a double zero- multiplicity 2), and 2

Find all zeros of the polynomial function by hand when given one zero to start. Example: x=3 so you know that (x-3) is one factor. So divide this into your polynomial with long division. Take your answer and factor to find the other zeros.

Your zeros were x= -5, x=3, x=4 Here they are on the graph.

Did not do yet Graph by hand- Change from standard form to factored form, find x-intercepts, decide if graph will bounce or cross at these values, find y-intercept, find points in between x-intercepts, scale the y-axis, use what you know about end behavior and U turns- graph.