1. For each polynomials, follow all the steps indicated below to graph them: (a) Find the x- and y-intercepts of f. (b) Determine whether the graph of f crosses or touches the x-axis at each x-intercept. (c) Describe the ends behavior as x gets closer to -  and  (d) Find the intervals on which the graph of f is above or below the x-axis. then sketch each polynomial and then determine (e) where the graph is increasing/decreasing. (f) where the relative extrema (maximum or minimum) are located. 1. f(x) = x(x − 2)(x − 4) Graphs and Behavior of Polynomials Name;______

2. 2.f(x) = (x − 2)(x + 4) 2 3. f(x) = x 2 (x − 2)(x + 2)

3. Challenge Problems: 1. Make up a polynomial that has the following characteristics: crosses the x-axis at -1 and 4, touches the x-axis at 0 and 2, and is above the x-axis between 0 and 2. Is this polynomial unique? Compare your polynomial with those of other students. 2. Make up a polynomial that has the following characteristics: degree 6; four real zeros, one of multiplicity 3; y-intercept 3; behaves like y = −5x 6 for large values of |x|. Is this polynomial unique? Compare your polynomial with those of other students. What terms will be the same as everyone else’s?