2. The “zero” of a function is just the value at which a function touches the x-axis.

3. We can find the zeros of a polynomial by setting each factor equal to zero. y = (x-2) 3 (x+3)(x-4) x – 2 = 0x + 3 = 0x – 4 = 0

4. When we graph polynomials, the exponent that goes with each zero matters. When a factor has a degree of 1, it “crosses” the x-axis. When a factor has a degree of 2 (or 4, 6, 8…) the graph “bounces” off the x-axis. When a factor has a degree of 3 (or 5, 7, 9…) the graph “flattens” along the x-axis.

5. Graphing a Polynomial Function 1.Determine the end behavior 2.Determine the zeros and plot them 3.Determine what happens at each zero 4.Draw a smooth curve

6. Example 1: Graph y = -(x – 3) 2 (x+4) 2 (x – 1)

7. Example 2: Graph y = 2(x + 4)(x + 3) 2 (x – 1) 3

8. Example 3: Graph y = -(x + 3) 4 (x - 7) 2 (x + 1) 3