1. Finding the Zeros of a Polynomial Function

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, then solving for x.
y = (x-2)3(x+3)(x-4) x – 2 = 0 x + 3 = 0 x – 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
Determine the end behavior
Determine the zeros and plot them
Determine what happens at each zero
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