Wetzel

Math 110

3.2 – Polynomial Functions of Higher Degree

Review of Polynomials –

                                                                        Degree             # of Solutions

Maximums / Minimums –

            Absolute Max. –

            Absolute Min. –

            Relative Max. –

            Relative Min. –

Other things to know –

            If any one the following statements are true, then they are all true.

• (x – c) is a factor of P(x)

• c is a real-number solution of P(x) and P(c) = 0

• c is a real-number zero of P(x)

• (c, 0) is an x-intercept of the graph of P(x)

Even and Odd Powers of a factor –

            Odd Power – the graph will intersect the x-axis at c

            Even Power – the graph will touch, but not cross the x-axis at c

Graphing a Polynomial -

            Steps:

            1.)  Find the y-intercept

            2.)  Find the x-intercept(s) or zeros noting the power of each factor

            3.)  Find additional points between the zeros

            4.)  Plot the points and sketch the graph

Open-Top Box Problem –

            A rectangular piece of cardboard measures 12 inches by 16 inches.  An open box is formed by cutting squares that measure x inches by x inches from each of the corners of the cardboard and folding up the sides.  

            a.)  Express the volume V of the box as a function of x.

            b.)  Find the length of the cut to the nearest tenth of an inch that maximizes the volume.

HOMEWORK:  6th Ed.  p.306 #1-5odd, 11-21odd, 33-37odd, 41-45odd, 61

                           5th Ed.  p.301  #1-5odd, 15-25odd, 33-37odd, 41-47odd