Step 1: Find zeros (xintercepts)
Step 2: Find yintercept, (substitute 0 in for x)
Step 3: Determine End Behavior
Step 4: Sketch the polynomial function by using Steps 13, and make a ttable(pick points in between zeros)
Sticking Point: Remember your parent graphs when you are sketching!!!!
Example 1
Step 1: Factor: x(x + 2)= 0 Identify zeros: x = 0, x = 2 
Step 2: yintercept = (0,0) 
Step 3: End Behavior: n is even, a > 0 Therefore: as x > +∞, f(x) > +∞ and x > ∞, f(x) > +∞ 
Step 4: Sketch the polynomial function. Plot Zeros, End Behavior, and remember Parent Graph: 
Example 2
Step 1: Factor:
Identify zeros: x = 0, x = 1, x = 1

Step 2: yintercept (0,0) 
Step 3: End Behavior: n is odd, a > 0 Therefore: as x > +∞, f(x) > +∞ and x > ∞, f(x) > ∞ 
Step 4: Sketch the polynomial function. Plot Zeros, End Behavior, and remember Parent Graph 
Example 3
Step 1: Factor:
Identify Zeros: x =0, x = 3, x = 1 
Step 2: yintercept (0,0) 
Step 3: End Behavior: n is odd, a < 0 Therefore: as x > +∞, f(x) > ∞ and x > ∞, f(x) > +∞ 
Step 4: Sketch the polynomial function. Plot Zeros, End Behavior, and remember Parent Graph 
Need to see more examples? Watch the video below on how to graph polynomials