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A. ___________ B. _____________ C. ______________ D. _______________ For each x-intercept, tell whether the graph is tangent to the x-axis (touches and turns) or crosses and continues through the x-axis? A. ________________________________________________________________ B. ________________________________________________________________ C. ________________________________________________________________ D. ________________________________________________________________ II. View the graphs below in a Zoom 4 window, sketch each, and identify the degree.  A.  EMBED Equation.DSMT4 (same as  EMBED Equation.DSMT4 ) degree?___ B.  EMBED Equation.DSMT4  degree?____  C.  EMBED Equation.DSMT4  degree?____ D.  EMBED Equation.DSMT4  degree?____ Observations: What similarities do you see in the shape of the graphs? _____________________________________________________________ What do you think caused the flip in the graphs of C and D? _____________________________________________________________ What do you notice about the degree of all the functions? _____________________________________________________________ Identify the x-intercept(s) of each graph. A. ___________ B. _____________ C. ______________ D. _______________ For each x-intercept, tell whether the graph is tangent to the x-axis (touches and turns) or crosses and continues through the x-axis? A. ________________________________________________________________ B. ________________________________________________________________ C. ________________________________________________________________ D. ________________________________________________________________ III. Based upon your observations above, predict the behavior of the graph of  EMBED Equation.3 . Sketch what you think the graph will look like on the coordinate plane provided. Do not use your calculator yet.  Now check your sketch by viewing the graph in the window shown. Comment on any inaccuracies in your graph. IV. Answer the following questions based on your observations of all graphs. Compare the graphs of polynomials of odd degree with those of even degree. What do you think this determines on your graph? Compare the factors with odd powers to those with even powers. What do you think this determines on your graph? Compare the equations with positive leading coefficients with those of negative leading coefficients. What do you think this determines on your graph? How do we determine the x-intercepts of a graph using only its equation? How do you think we can determine the y-intercept? V. Try these without using your calculator: Using what you have learned, match the equations to their appropriate graph.  Graph: _______ Graph: _______ Graph: _______ Graph: _______ A. B.   C. D.   In the space provided, sketch a graph of the equation without using your calculator. Note the x-intercepts and y-intercept on the axes. You need not worry about proper scaling on the y-axis. 5.  EMBED Equation.3  6.  EMBED Equation.3    7.  EMBED Equation.3  (Hint: Notice that all the other polynomials weve studied have been written in factored form!)  8. Now, write an equation for a polynomial whose graph has the following characteristics: As  EMBED Equation.3  and as  EMBED Equation.3  The graph is tangent at both its x-intercepts -5 and 2. Write your equation here:__________________________________________ What is the y-intercept of your graph?____________ Challenge: You must be a pro by now! See if you can handle this one! 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