Graph sketching polynomial functions.

1. Curve Sketching
A treasured sketch !! :) by flickr user atinirdosh

2. Solve by factoring each polynomial completely.
3
(a) x + 5x 2 + 2x - 8 = 0

3. Solve by factoring each polynomial completely.
3
(a) x + 5x 2 + 2x - 8 = 0

4. Solve by factoring each polynomial completely.
(d) 2x3 + 7x 2 + x - 10 = 0

5. Graphing Polynomial Functions
ƒ(x) = x n
Appearance
Where n is odd, the
Where n is even, the
graph looks like this:
graph looks like this:

6. Graphing Polynomial Functions
Roots
The maximum number of roots for any polynomial function is
equal to the degree of the function.
Examples: Cubic Quartic Quintic
3
ƒ(x) = x 4 ƒ(x) = x 5
ƒ(x) = x
max. # of roots 3 4 5

7. Graphing Polynomial Functions
Sketching
Step 1: Find the y-intercept (let x = 0)
Step 2: Find all roots. (Use rational roots theorem if necessary.)
Step 3: Determine the sign of the function over the intervals
defined by the roots.
Step 4: Sketch the graph

8. Solve by factoring each polynomial completely.
3
(a) x + 5x 2 + 2x - 8 = 0